Age of Wonders series - great TBS with a magic research tree, fun story and humour.
Master of Orion series - another great TBS, kind of like Civ in space (except that doesn't do it justice)
UFO:Aftermath/UFO:Aftershock - humanity trying to survive after alien invasion, switching between strategical - base building, research etc, mode and tactical mission mode
Witcher series - bringing RP back to RPG, amazing story, characters, decisions that actually matter for once and have long reaching consequences, beautiful visuals and interesting setting with a touch of dark and grim realism.
Max Payne series - an FPS (well TPS actually) masterpiece, great story, characters, setting and good gameplay.
Hitman series - assassination simulator if you aren't familiar, a stealth shooter that does stealth right - you can pass 99% of the obstacles without shooting a single bullet, but if you fail to be stealthy you can still succeed 99% of the time by going in guns blazing.
Thief series - another game that does stealth right (hell it invented the stealth genre), a stealth shooter, the objective is to steal stuff and not get caught/killed in the process. If you're good, noone will know you were even there, but if you're not you can still complete the mission most of the time.
Baldur's Gate series - an iconic RPG that mixes well translated 2ed D&D mechanics with a superb story and unique characters.
Fallout series - post apocalyptic RPG that delivers great story, great gameplay and manages to be both funny and grim at the same time. I suggest 1+2, 3 wasn't bad but it really doesn't compare to 1+2 both in freedom and in humour. Fallout Tactics wasn't bad either - reminiscent of 1 and 2, but mostly in missions format and all about tactics while the RPG aspect is almost non-existant.
Arcanum - an RPG in a setting where magic and steamwork technology live side by side, mechanics are similar to baldur's gate and fallout (1+2). Great characters and story, fun combinations of spells and tech.
Freelancer - not sure how to describe the genre besides space flight sim with elements of trading and combat, fun story, interesting missions, freeroaming exploration. I wish there were more games like this one, take it as a recommendation.
Yakuza series - a game with a very Japanese setting, bordering on the stereotypical, a third person fighting game with yakuza members as main protagonists, think gta without cars and mostly without guns except with lots of hand to hand and a bunch of fun minigames and entertaining (sometimes dramatic, sometimes goofy) missions.
Dawn of War:WH40k - an RTS in the WH40k setting that throws away most resource gathering mechanics and replaces them with area control (which in turn give resources), which streamlines the battles (in a good sense, not in the "we cut away everything that was interesting about the genre" kind of way), big choice of varied armies (original is mostly story based, expansions let you pick pretty much anyone you want) each fun in its own way.
Warlords:Battlecry series - a fun RTS in a fantasy setting with lots of armies to choose from, features hero units that progress from mission to mission predating the hero units in warcraft 3.
Hacker Evolution - hard to describe, basically a hacking simulator in a shell environment, where you hack different servers in order to find out information and gain money for upgrading you equipment (read PC hardware), with an overarching story from mission to mission.
Blood Omen: Legacy of Kain - an action adventure game with superb setting, story, characters and dialogue. You play as a newly reborn vampire with a burning desire for revenge, on your way you battle forces that threaten to destroy the world.
Heroes of Might and Magic series - (I suggest 1+3+5) a TBS classic, a fantasy setting with a big choice of spells and units.
Need for speed 5: Porsche - a well done racing game, with a few different game modes, a nice choice of vehicles.
Vampire the Masquerade - (Redemption in particular, but Bloodlines is good as well) an RPG about vampires, their secret societies, their internal and external struggles. Redemption and Bloodlines tell different stories in the same setting (for the most part - Redemption starts in medieval and continues to modern day, while Bloodlines is all in the modern day). Interesting story, great music, fun and unique characters. Its hard to summarise. The main protagonists in both games are newly turned vampires, that try to reach their own goals while being pawns in everybody's elses games. Redemption is much more story driven, Bloodlines is much more action driven.
SWAT 4 - a unique shooter in that your goal isn't to kill everybody around you, but to mostly arrest the bad guys and save the innocents.
Mount and Blade series - a medieval simulator (yes, its hard to describe), mostly lacking story, a big focus on battles and trading, has different quests, different kingdoms with different soldiers.
Magicka - a fun action game with almost endless amount of magic combinations.
Majesty series - I'd say this was an RTS but it isn't, its a fantasy kingdom simulator, basically you play as the king and don't control anything directly, instead you issue orders and offer rewards, build different buildings to attract adventurers and boost your economy, all in order to protect you kingdom. Good music, nice light hearted humour, a refreshing change from the RTS games out there.
Assassin's Creed series - third person action game with a plot that can break your mind, good music, well done and fun gameplay, beautiful architecture (first had gameplay issues, mostly repetetive missions but is an intro to the story).
E.Y.E.: Divine Cybermancy - another one that's hard to describe, an FPS where hacking has a major role, from security systems to other people's brains. Fun choice of weapons and powers.
Jedi Knight:Outcast/Jedi Academy series - an action/shooter game in the Star Wars universe, the story is ok but the gameplay is great, both in jedi powers and weapons.
Knights of The Old Republic series - an RPG in the Star Wars universe, a rare jewel that combines pretty much everything that's awesome about Star Wars with great story and memorable characters.
Neverwinter Nights series - another great RPG using 3ed D&D rules, I personally prefer the second - it makes more sense adventuring as a party rather than alone, but its said to have an enormous amount of bugs (again, I personally have been lucky enough not to encounter them).
Red Dead Redemption - a story driven shooter in the wild west with fun mechanics and loads of minigames.
Command & Conquer: Red Alert series - a great RTS that doesn't take itself too seriously, fun story and units to the point of being wacky and going beyond stereotypical.
Command & Conquer: Generals - another good RTS, while not as "fun" as red alert, its nevertheless very well done.
Total Annihilation - another good RTS.
Aliens versus Predator 2 (2001) - great FPS, both in single player campaign and in multi player matches.
Fighting Force - a good 3D (not in the cursed sense 3D is used nowadays but the way it was used in the 90s) fighting game, think Streets of Rage or Final Fight in 3D environment.
