I have used a lot of free .NET libraries, some from Microsoft itself! Which ones have you found the most useful?
Package managers for external libraries
Dependency Injection/Inversion of Control
Design by Contract
Automated Web Testing
Misc Testing/Quality Support/Behavior Driven Development (BDD)
MS Word/Excel Documents Manipulation
Please provide links to these free libraries as well. Once we have a huge list of this, it can be arranged in categories! Please do not mention .NET Applications/EXEs here.
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ELMAH (Error Logging Modules and Handlers) is an application-wide error logging facility that is completely pluggable. It can be dynamically added to a running ASP.NET web application, or even all ASP.NET web applications on a machine, without any need for re-compilation or re-deployment.
Update: To work with Asp.Net MVC  http://code.google.com/p/elmah/
The Microsoft .NET Framework . I'd never get any work done without its libraries. http://msdn.microsoft.com/en-us/netframework/aa569263.aspx
In-process database servers make my life easier.
Subsonic . An open source object-relational mapper. http://subsonicproject.com/
Microsoft Chart Controls  for Microsoft .NET Framework 3.5 http://www.microsoft.com/downloads/details.aspx?familyid=130F7986-BF49-4FE5-9CA8-910AE6EA442C&displaylang=en
I have found that the C5 Collections  library is the most extensive and well designed collections framework for .NET. http://www.itu.dk/research/c5/
For me, by far and away the single most useful library is:
Perfect for websites on a shared hosting package with fairly "light" database needs. http://sqlite.phxsoftware.com/
AForge.NET is a C# framework designed for developers and researchers in the fields of Computer Vision and Artificial Intelligence - image processing, neural networks, genetic algorithms, machine learning, robotics, etc. http://www.aforgenet.com/framework/
Word / Documents:
Excel XML Writer  allows creation of .XLS (Excel) files. No Microsoft Office necessary. Been a while since it has been updated. It also provides code generator  to create code from already created XLS file (saved as xml). Haven't tested this but looks very promising. Too bad author is long time gone.
Excel Reader  allows creation/reading of .XLS (Excel) files. No Microsoft Office necessary. Been a while since it has been updated.
Excel Package  allows creation/reading of .XLSX (Excel 2007) files. No Microsoft Office necessary. Author is gone so it's out of date.
EPPlus  is based on Excel Package and allows creation/reading of .XLSX (Excel 2007). It is actually my favorite when it comes to Excel. It's actively developed and so far have been able to do most things i needed (which I can't say the same about 3-5 packages), but it's only limited to .XLSX (which from one side is good thing). I'm still testing it thou :-)
NLog  for logging http://www.nlog-project.org/
Dependency Injection: Ninject 
Web MVC framework: ASP.NET MVC  (1.0 released yesterday!)
Client MVP-ish (or is that MVVM?) framework: patterns & practices Composite Application Guidance for WPF and Silverlight, aka Prism  (v2 released Feb 2009) http://ninject.org/
For PDF, other than PDFSharp,
iTextSharp  http://itextsharp.sourceforge.net/
Lucene.net  -> For text indexing/searching http://incubator.apache.org/lucene.net/
A free high quality charting library for .NET supported by Microsoft. http://code.msdn.microsoft.com/mschart
Recaptcha  - captcha control
url rewriter  - open source URL rewriting
UrlRewriting.Net  - another URL rewriter
GoogleMaps.Subgurim.NET  - Google maps server control http://recaptcha.net/plugins/aspnet/
I've created a new library for making it easier to consume REST APIs in .NET: RestSharp  http://restsharp.org
Nini  is an uncommonly powerful .NET configuration library designed to help build highly configurable applications quickly. Generally it is about INI files. http://sourceforge.net/projects/nini/
ZedGraph  for graphing. http://zedgraph.org/wiki/index.php?title=Main%5FPage
Krypton Toolkit  - Windows Forms Controls http://www.componentfactory.com/free-windows-forms-controls.php
HTML Parsing : Html Agility Pack  http://htmlagilitypack.codeplex.com/
I do not think these have been mentioned
"Through a fluent, extensible interface, NBuilder allows you to rapidly create test data, automatically assigning values to properties and public fields that are of type of the built in .NET data types (e.g. ints and strings). NBuilder allows you to override for properties you are interested in using lambda expressions." http://nbuilder.org/
I'd like to add AutoMapper  to the list, as tooling. It's so useful if you are doing any kind of application development where you are mapping DTOs or Update/View Models to domain object. It is convention based, and lets you do some awesome object mapping so easily. http://www.codeplex.com/AutoMapper
IKVM  brings the extensive world of Java libraries to .NET. http://www.ikvm.net/
OpenNETCF , essential if you're working with Compact Framework and makes work there much less gruesome. http://opennetcf.com/
I can't believe nobody suggested FluentValidation  so far. http://fluentvalidation.codeplex.com/
Well, Jon Skeet's MiscUtil , of course! http://www.yoda.arachsys.com/csharp/miscutil/
DotNetZip  for ZIP file handling. http://dotnetzip.codeplex.com
For 3D graphics OpenTK is probably the best for OpenGL .
Unclassified (specifically, serialization)
ExcelLibrary  is a really light and simple library to create and read .xls file. It has little formatting options though.
Code example to export a dataset to an Excel file :
Since you added LinqToTwitter I think it would only be fair to add the following libraries
A .NET client library for the Facebook API that allows developers to create Facebook Applications in C# and VB.NET with support for ASP.NET and ASP.NET MVC.
For all your syndication & social networking needs
I'd add The Object Guy's .NET Logging Framework  (Bitfactory.Logging).
Compared to many others, it's quite lightweight - extremely quick and easy to set up, and will more than cover all the necessary bases for many projects that don't want/need the complexity of some other logging frameworks. http://www.theobjectguy.com/DotNetLog/
NAudio  is audio and MIDI library.
PetaPoco , a tiny, fast, single-file micro-ORM similar to dapper-dot-net http://www.toptensoftware.com/petapoco/
DevExpress has 60 free controls (both ASP.NET and WinForms)... definitely check them out...
Thanks :) http://www.devexpress.com/Products/Free/WebRegistration60/
You've got all of my favorite libraries covered. Here is my humble attempt to share a collection of utilities I wrote over the years and reused across various projects:
This collection includes helper classes for ASP.NET web forms (time localization, etc), Windows services, error reporting, and more. Please read help file for detailed description and examples.
UPDATE: I just discovered a multi-purpose utilities library  by James Newton-King, which looks pretty handy. http://alekdavis.blogspot.com/2009/06/myutilities-class-library.html
If you want to embed a small, fast, easy to learn and very poverful scripting language in .NET applications, this is the way to go.
Visual Web Gui 
The SDK includes the complete WinForms Toolkit, 58 WinForms Controls and integration into ASP.NET. It also includes the revolutionary Visual WebGui runtime which enables desktop application-like responsiveness and heavy-lifting abilities for data centric web applications supporting multiple presentation layers* from the same source code. http://code.google.com/p/luainterface/
nHibernate sharp zLib
(Sorry if this has already been posted.) http://en.wikipedia.org/wiki/Object-relational_mapping
Open Source Enterprise Service Bus Projects:
Mass Transit - http://masstransit.pbworks.com/
NServiceBus - http://www.nservicebus.com/
Spark View Engine  - a really good ASP.NET MVC (and not only) open source view engine. http://sparkviewengine.com/
XML-RPC.NET  by Cook Computing - A great open source XML-RPC library for dealing with services like Pingbacks and MetaWeblog API.
NVelocity  by the Castle Project - Super powerful templating library.
Janrain OpenID library
More of an XNA specific one but Farseer Physics  is a great XNA 2D physics library. http://farseerphysics.codeplex.com/
A great free Silverlight Charting library: Visifire  http://visifire.com/
HTML Agility Pack . For scraping HTML and accesing it as XML.
Disclaimer: I'm also biased. :) http://en.wikipedia.org/wiki/Line%5Fof%5Fbusiness
Glimpse  - What Firebug is for the client, Glimpse is for the server. http://getglimpse.com
SharpNLP  Handy for a spot of Natural Language Processing
Noticed NuGet was added as a package manager
OpenWrap  - its another open source package manager (I am not sure if this has been mentioned before) https://github.com/openrasta/openwrap
two other cool free libraries I haven't seen in the list yet:
And I don't remember if someone mentions Json.NET ... If not, here's the link ! http://npoi.codeplex.com/
SharpPcap  - .NET pcap wrapper to capture and parse network packets http://sourceforge.net/projects/sharppcap/
IBatis  is also XML-based Object/Relational mapping and persistence framework as well as a data access abstraction layer.This framework is available for .Net as well as Java too. http://ibatis.apache.org/
NodeXL  is a great open source library for computing and visualizing Network graphs. It includes an Excel template and a .NET library with a presentation library in WPF. http://nodexl.codeplex.com/
Another useful ORM framework: ADO.NET Entity Framework  http://msdn.microsoft.com/en-us/library/bb399572.aspx
Caliburn  (a client framework for WPF and Silverlight) should certainly be in here. http://caliburn.codeplex.com/
I found usefull the following:
CruiseControl.Net ? - I don't think that's listed already?
Blogger APIs 
Google Chart API  http://blogengine.codeplex.com/releases/view/39387
DotNetTransitions  is a library that does control animation and transitions in a WinForm application. Very smooth and easy to use. http://code.google.com/p/dot-net-transitions/
FileHelpers - http://filehelpers.sourceforge.net/ A Professional way to handle csv files and other separated documents into objects.
Xsd2Code - http://xsd2code.codeplex.com/ Good one to deal with XMLs. You can create objects from Schema and a professional way to read and write XML.
Sprite and Image Optimization Framework  for optimizing the website images
Currently still at Preview 2
It's a part of the ASP.NET MVC Framework project on codeplex, Works fine with WebForms too http://aspnet.codeplex.com/releases/view/50869
I think FluentMigrator  for database migrations is one of the most useful libraries out there. It's based on Ruby Migrations and is a great way to version control database changes. https://github.com/schambers/fluentmigrator/
uhttpsharp  - a very basic embedded http server for .net. http://code.google.com/p/uhttpsharp/
Postal , this is a useful email generator based on MVC 3 and the Razor syntax. Provides an easy way of sending emails as well as dynamically creating emails. http://aboutcode.net/postal/
Gallio/MbUnit  for unit testing. http://gallio.org/
ORM - Sooda (http://sooda.sourceforge.net/)
Sooda is object-relational mapping  software for the .NET (http://msdn.microsoft.com/net) environment. It lets you automatically generate an object-oriented data access layer (DAL) for your application. Instead of writing SQL code, you can now focus on writing business rules in object-oriented .NET languages.
Sooda is an open source software distributed under the terms of the BSD license.
I strongly recomend NLog which is very easy to use and very fast. http://en.wikipedia.org/wiki/Object-relational%5Fmapping
The Free and amazing SourceGrid  http://www.codeplex.com/sourcegrid/
Microsoft Learning Components from Microsoft's SharePoint Learning Kit (www.codeplex.com/SLK) (E-Learning/SCORM libraries).
FreeImage.Net (freeimage.sourceforge.net/download.html) (.NET wrapper for FreeImage) -- I use this to get 4:4:4 subsampling for saving JPEGs.
(Can't post proper links yet.) :)
These are the ones of those listed that I've found useful:
(We use another O/RM, but it's no longer maintained.)
This is not to say that I've fully evaluated all of the alternatives!
Other libraries of note:
HtmlAgilityPack  (easy parsing of HTML)
Wow, this is hard if you leave out the EXEs and add-ins! :) http://www.codeplex.com/htmlagilitypack
DevExpress  also has a free set of controls. http://devexpress.com
From their homepage:
Iridium is the numerical foundation of Math.NET, aiming to provide commonly used mathematical elements for scientific numerical computations. It offers the infrastructure for basic numerics, linear algebra, random generators and distributions, integral transformations, etc.
What I've used it for is PCA (Principal Component Analysis) (eigenvalue decomposition) which worked like a charm. License: LGPL. Self-contained (no extra dependencies).
Quartz.NET  - Enterprise Job Scheduler for the .NET Platform. http://quartznet.sourceforge.net/
The Fast Artificial Neural Network Library (FANN) found at http://leenissen.dk/fann/ is great.
Nice list all.
Two that have not been mentioned that I use a lot are:
I use the Spring Framework  and quite like it for dependency injection.
The Ventaur Web Page Security project (available here: http://www.codeproject.com/KB/web-security/WebPageSecurity%5Fv2.aspx) is incredibly useful for (ASP, admittedly) .NET.
Please correct me if I go wrong with Microsoft.ReportViewer . http://www.gotreportviewer.com/
TA-Lib  for those who love trading stocks using technical analysis. http://www.ta-lib.org/
NBug  (Open source) - Automated bug, error, and exception reporting tool (with minidump generation capabilities). We use it most of our dekstop applications/projects (once it was just an internal tool). http://www.nbusy.com/projects/nbug
NDesk.Options , Command line arguments parser.
Examples here  http://www.ndesk.org/Options
Caliburn.Micro  - A small, yet powerful framework designed for WPF, Silverlight and WP7.
NotifyPropertyWeaver  - Uses IL weaving to inject INotifyPropertyChanged code into properties. http://caliburnmicro.codeplex.com/
PDF Clown for PDF creation/manipulation.
Math.NET Numerics  - From the homepage,
Math.NET Numerics is an open source numerical library for the .NET Framework and Mono.
Numerics is the numerical foundation of the Math.NET project, aiming to provide methods and algorithms for numerical computations in science, engineering and every day use. Covered topics include special functions, linear algebra, probability models, random numbers, interpolation, integral transforms and more.
Numerics is the result of merging dnAnalytics with Math.NET Iridium and is intended to replace both. It targets Microsoft .Net 4.0 and Mono, and in addition to a purely managed implementation will also support native hardware optimization.
Twitterizer  - A twitter API. http://www.twitterizer.net
Piczard FREE Community Edition  - .NET image manipulation library (WYSIWYG image crop, resize, rotate/flip, color adjust, etc...) http://piczard.com
Wintellect's Power Collections for .NET  provide several nice complementing generic collections and algorithms to the .NET framework ones, including (but not limited to): Deque, Bag, OrderedBag, Set, OrderedSet, Binary Search, Generate Permutations, etc.
Could go in the same category as C5 Collections. http://powercollections.codeplex.com/
Here is our free stuff (from Kellerman Software):
Free Wrapper for SharpZip that zips directories: http://www.kellermansoftware.com/p-19-free-sharp-zip-wrapper.aspx
Library to perform deep compare of two .net objects: http://comparenetobjects.codeplex.com/
Library to run NUnit on Windows Phone 7 http://nunitwindowsphone7.codeplex.com/
Genuilder - Amazing code transformation library allowing creation of DSL, syntax enhancements AOP - http://genuilder.codeplex.com/
There are a couple of other ORMs that I think should make this list:
CoolStorage  is one. It works on iPhone and Android as well (using Mono) which is pretty cool.
Another is Simple.Data  which looks very much like Active Record of RoR fame. http://viciproject.com/wiki/projects/coolstorage/home
Take a look at the data mapper I have on codeplex, Mapper Extensions . Feel free to add it to the list if you find it useful :) http://mapperextensions.codeplex.com/
What about .NET PowerCollections? Or are C5 Collections which are already listed better?
Sharp SVN  for Subversion operations is very good. http://sharpsvn.open.collab.net/
NMock2 for unit-testing/mocking. NMock2 
Lucene.NET: an open-source .NET port of a popular search engine API. Lucene.NET  http://www.nmock.org/
Zodiac.NET  is a good framework for building forms, surveys and questionnaires from XML. http://www.mentor-logic.com/index.php/products/components/zodiacnet
I would also recommend the book
:Windows Developer Power Tools: Turbocharge Windows Development with More Than 140 Free and Open Source Tools (Paperback)
Not only does it list a lot of tools it also provides information on how to use them etc. in one place.
link text  http://rads.stackoverflow.com/amzn/click/0596527543
Some that haven't been mentioned:
I've found that SharpZipLib is slow and doesn't compress nearly as good as winzip. I've used the C# version of 7-zip's LZMA algorithm is muuuch better.
Log4Net  http://www.nunit.org/