Several games got my vote:
Unreal, for simply put being one of the best Singleplayer experiences of its day, right up there with Half-Life. Unreal made a whole world of mysterious flora and fauna seem believable, and its AI was superior to Half-Life's in most regards.
Unreal II, despite what most will say, was a fine FPS, and a pretty one, too. Its main problem was that it essentially ditched any links to the original game save the Skaarj and a few vaguely familiar weapons. If it were named anything else, it probably would've been better received by the fanbase.
Unreal Tournament, there is nothing I can say here that others haven't, and is probably the best out of all the overall entries. It was fast, it was frantic, the AI was fiendish and the strategy of the gameplay simply outweighed, outclassed, and outdid any other twitch MP Shooter of the day - and indeed, it still can probably hold its own on the gameplay department.
UT2004, was a good way to shore up UT2003's faults, as well as introduce some new things (Vehicles) while giving it the appropriate spin. And it worked... until 2006, when most people found out that they couldn't one-hit kill vehicles with shock combos and so abandoned the gametype for the most part, proclaiming vehicles were for noobs and retreating to the safety of DM-Rankin and DM/CTF-Grendelkeep, which were far more favorable matchups for hitscan games.
Unreal Tournament 3, is a lot like UT2003 in many ways. As I said on IRC the other night, UT2003 had everything but the gameplay perfect. UT3 had everything but the gameplay FUBARed. While the gameplay itself is very solid and just as fun as the original UT's, too many people were turned off by the horrid menu, lack of features, bad launch, lack of Warfare in the demo, little bugs and issues, no Linux server, still no Mac and Linux clients, framerate-sensitive aiming, STILL no lag compensating netcode... the list goes on and on. Throw in
very stiff competition in the form of COD4, TF2, and Crysis, and Midway likely pushing Epic a bit for a release, and of course, the fateful decision to let Gamespy handle the Master Server and it simply added up to too many annoyances to outweigh the positives of the game. There's a good game in there despite all of this, though, which gives me hope for...
Unreal Tournament 4. If Epic has taken this criticism to heart - and I'm very sure they have, and likely some of them are privately just as frustrated with its reception as they are, then the next UT is their chance to either say we were right and they don't care, or that we should shut the **** up because they will deliver a game that will dazzle us all. I'm pretty convinced that, like UT2003, UT3 was a victim of its own lofty expectations, failure to meet those, ideas that got announced and scrapped, and pressures to deliver, and when it came out in the state that it was released in, it naturally failed to meet those. Epic proved they can learn from their mistakes with UT2004, and I see no reason they can't do it again... but if UT4 (Or UT3.5, or however they decide to do it if they do do it) is to be a success, it needs to have tight lips kept on its features until they have something to show, it needs to fix all the things that went wrong with UT3 (Menu, gamespy, lack of features, etc), and - perhaps most importantly - it has to be polished, not rushed. We all know Epic is under contract to do three Unreal games with Midway. (Anthology doesn't count, IIRC.) UC2 was one, UT3 was two. This means we might get a UT3.5/UT4, or a Unreal III (Which also needs to go back to its roots, but that's a different topic entirely) but it means we should see at least one more Unreal game. And Epic is not a company that doesn't learn from its mistakes.
Apologies if this was tl;dr. But people really need to stop running around like Chicken Little, and taking everything that is said or whispered at face value. If anything, now is the time to be showing we still stick by them because we still believe they can put something out that is more attractive to more people. UT3 tried to capture it, but it didn't, so UT3.5/UT4 simply MUST do it. Fortunately, things like a new interface are much easier to take care of than complete tweaking and rebalancing of game mechanics.