Depends on what you like.
4X strategy:
-Civilization IV. Best in the Civ series, though with Gods and Kings 5 gets close. Get the Beyond the Sword Expansion, and its amazing, with a few great mods out there too. All turn based, on a regular square grid.
-Any Total War game [Though I remember hearing Empire wasn't as good as it could have been, though you'll have to ask someone else on that]. Great grand strategy games, with tactical combat carried out in real time with some reasonable level of depth.
RTS:
-Starcraft 2. Fast paced, quite well balanced, massive online community, focused on Multiplayer but has a single player campaign. Small scale overall.
-Sins of a Solar Empire: Rebellion. Very slow paced [Games take several hours to complete most of the time], rather poorly balanced overall [Against the AI you don't notice all that much though]. Small online community that dependent on who you get in a game can be hostile to new members, but not always. Focused on Single Player, has no campaign. Massive Scale.
FPS:
-Battlefield 3. If you're looking for one of the newer 'Hyper realistic' [Lolwat] FPS games, BF3 is the go to. Vehicles, terrain destruction, large maps and 64 players help the gameplay, whilst the graphics are absolutely stunning.
-Tribes Ascend. If you don't like modern hyperealistic shooters, this is probably the best go to in modern times. Interesting play mechanics with skiing, and guns that don't have instant travel bullets, and if they do then they deal pathetic damage. Quite fun all in all.
-Black Mesa. Half Life 1 Remake in the Source Engine. If you want an FPS focused on the campaign, with great atmosphere and with occasional breaks from just shooting things for you to complete other tasks [Some minor platforming, solving some minor puzzles], this is definitely the go to game.
Sandbox:
-Batman Arkham City. Looks great on the PC, very well polished and is fun to play. Not much more to say - the combat is a joy, the story is good and it paces itself well - as well as actually having a couple of good boss fights.
-Sleeping Dogs. Looks amazing on the PC [Shaders and reflections anyway, especially in the rain. Textures are ok, but faces look kinda bad IMO compared to some other PC titles]. Fun to play, somewhat interesting story, and all of Hong Kong to treat as your playground. In addition, the driving being overly arcady means it controls ok on the PC in that department, and it can be hilarious some of the things you do.
Other than that, I'll leave it for you to decide. RPGs are these days too broad in what people consider to be and not to be RPGs to be able to give a decent recommendation, MMOs I hate and don't play, and most other types of games I generally ignore.