I've always loved "turn-based tactical" games, the kind that are played on a grid.
Some examples of my favorites from this genre are:
However, I haven't seen new games of this type in years, and I seem to have played them only on my old consoles / handhelds. Recently I stumbled upon a free web game called HRmaggeddon [1], which I had a blast playing for a few weeks, but it still seems tough to find them.
What are some good games of this genre for the PC?
Clarification:
Based on some of the answers below, it seems I've been a bit ambiguous with this question, so I'll attempt to clear it up. When I say "played on a grid", I mean specifically the battle system, not games that have traditional RPG gameplay in battle, but have tile-based "world maps" (example, Final Fantasy 1 isn't the type of game I'm talking about).
X-Com. The original, DOS game. Can be picked up for 2-5 bucks on Steam. Squad-based turn-based tactics game.
It can be pretty brutal on a first timer though (especially Terror from the Deep)
Battle for Wesnoth [1] is free, and there's a Windows, Mac, and Linux version. It has online multiplayer and TONS of content (and even more user-submitted content).
[1] http://wesnoth.org/Heroes of Might and Magic III
Has both strategy and tactical elements. Available at good old games for a measely $10: http://www.gog.com/en/gamecard/heroes_of_might_and_magic_3_complete_edition
The HOMM series are good, HOMM 3 already mentioned above. If you end up liking those, check out King's Bounty [1] on Steam.
[1] http://www.kings-bounty.com/Jagged Alliance 2 [1] is an excellent turn based tactical game. You can pick it up on both Steam and GoG (unfortunately since I don't have 10 reputation I can't give you direct links).
[1] http://en.wikipedia.org/wiki/Jagged_Alliance_2The old classic- Masters of Orion!
Fallout: tactics
You might want to have a look at Space Rangers 2 [1] and its expansion. It's an odd ball mix of RPG, text adventure, Elite, turn-based gameplay and even real-time strategy, but it all really work pretty smoothly. It got a lot of replayability since you can embrace pretty much any career you can think of in a space game (privateer, pirate, trader, police...) And it's the only game I can think of where NPCs can actually beat the game before the player.
[1] http://en.wikipedia.org/wiki/Space_Rangers_2Warlords was nice when it started (warlords 2 & 3 especially). But from there they pretty much went downhill.
Warlords ... http://en.wikipedia.org/wiki/Warlords_(game_series) [1] ... is the one that got me hooked. I got so addicted to this game I didn't sleep for days at a time!
[1] http://en.wikipedia.org/wiki/Warlords_%28game_series%29Batallion Nemesis [1] is a flash spinoff of advance wars. I quite like it. If you click the "related" link toward the bottom left, you can see other games in the series.
[1] http://www.newgrounds.com/portal/view/459232Panzer General Forever [1]is a free remake of PG that I've been having fun with lately.
Armageddon Empires crypticcomet.com/games/AE/armageddon_empires.html is a bit different than games you listed because it is a bit more 4X and the hex by hex movement is less important, but it's certainly turn-based and tactical, with resource collection, tanks, aircraft, supply routes, giant robots, assassins, heroes, technological and biological upgrades, nukes, and dinosaurs.
[1] http://panzercentral.com/forum/viewtopic.php?t=45039Try out Weewar [1] - it is an online multiplayer turn-based strategy game, not too different from Advance Wars, or so I've heard. It is played in the browser so no download required. You control various units on a hex grid with varying terrain, leaving open lots of room for different strategies and tactics. Games can be slow or fast-paced to fit your daily schedule. Definitely worth a look. Hope this helps. =D
Disclaimer: I am currently doing an internship with their developers.
[1] http://weewar.comFallOut 1,2,3. (it's more of a RPG, but..)
It's a delicate mix of strategy, RPG, adventure and it's just tons of fun.
Imperialism and Civilization also have that, I believe, though the focus is on the city building stuff.
The Silent Storm series, as I have outlined in this answer [1]. To summarize it: very good small-team tactical, turn-based game, with some emphasis on realistic wounds, unit placement and destructible environments.
[1] http://gaming.stackexchange.com/questions/1566/what-games-are-similar-to-the-jagged-alliance-2-series/1602#1602Here's one I'd recommend that no one has mentioned yet: Jeanne d'Arc [1] on the PSP.
Otherwise, I also recommend these games that others have mentioned:
I've also heard good things about the Disgaea series (PS2/3 and PSP) but never really managed to get into it.
[1] http://www.metacritic.com/games/platforms/psp/jeannedarcI know thar someone has mentionned Civilization but I think that freeciv [1] deserves to be mentionned. It's free and you can play alone or online.
[1] http://freeciv.orgCivilization or Hearts of Iron 3 are the two big ones at atm
On the MMORPG side, Atlantica [1] uses the "tactical turn-based rows-of-people" model for combat. I stopped playing it due to the grind (I honestly don't have the patience for MMOs), but if you like MMOs and turn-based combat, this could be for you. (Side note: if you don't move fast enough, your turn ends, but a minute is easily enough to get everything done with time to spare.)
[1] http://atlantica.ndoorsgames.com/center/default.aspNot on PC, but if you are a fan of TRPG you should get ahold of Disgaea. You can get it on PS3, PS2, PSP and NDS. In various version/sequal between 1 and 3.