My university name is "FJFI", with e-mail/web addresses containing lowercase "fjfi". Then "fi" gets ligatured whereas "fj" does not, and the result looks a bit strange. My question is, which possibility would you choose:
Below you see the shapes in Computer Modern and New Century Schoolbook, the second one is with forbidden ligature (for comparison).

ACCEPTED]
Here's a horrible, completely wrong way to get a "fj" ligature that will only work with Computer Modern. A proper way to solve the problem would be to get (or create) a font that has the ligature. Latin Modern may have this ligature in the future [1].
\documentclass{article}
\usepackage{xcolor}
\newcommand{\fj}{%
% Use the 'fi' ligature
fi%
% Erase the 'i' part
\llap{\textcolor{white}{\rule[-0.05em]{0.252em}{0.55em}}}%
% Overlay a dotless j instead
\kern-0.01em\llap{\j}%
% Kern back a little
\kern-0.05em\relax}
\begin{document}
fi\fj
\end{document}

As per Andrey's comment, I formulate this as an answer: I see two ways you could go:
Just to give you an idea: in ConTeXt mkiv, using this ligature is as simple as this:
\usemodule[simplefonts]
\setmainfont[MinionPro]
\starttext
fifj
{\it fifj}
{\bf fifj}
{\bi fifj}
\stoptext
Which looks like this:

fontspec's manual section IV.12.1 to get fj replaced with the proper ligature while typesetting. - Florian
"fj" should absolutely be typeset with a ligature (for these fonts). The reason it is not is simply because "fj" is very uncommon in English.
In Garamond "fj" looks horrible.
cmrfor math texts and I would like not to change this, but I'm open to any ideas ;) - yo'\charXYZ, just I cannot find the symbol in my LaTeX fonts... - yo'filigature. Using a fixed width font for email addresses guarantees this. - egreg\ttsolves all. Broken ligatures doesn't look nice, even in this example, and when I came to this, I thought about it as about a more general problem than my "fjfi". - yo'