Okay, this might be a longish list, so bear with me. :p
RPG's:
Planescape: Torment - not only is this often hailed as the best RPG ever made, it has also been rereleased recently so it shouldn't even be that tough to find.
Neverwinter Nights 1 & 2 + addons - the campaigns on the main games are nothing special, but the expansion packs are marvelous. Especially Mask of the Betrayer, which stands up to Torment in sheer quality. Dragon Age: Origins is also something to consider.
The Fallout series - Huge postapocalyptic worlds to explore, with dark humour, great dialogue, and a freedom of choice that completely overshadows modern so-called "open world" games.
Arcanum - Basically Fallout games, but in a different setting.
Point and click-games:
Sam & Max - Hit the Road, and series 1 & 2 - Hell, pick up the source material if you can find it. Good games with excellent humor.
The Dig - Basically what a good Spielberg movie would look like if directly imported into game form.
Blade Runner - If you're into the movie, you'll love this one.
Space Quest/ Leisure Suit Larry - boxsets - Arguably the best Sierra point-and-click games ever made.
Discworld games - These might be a pain to find, and can be quite incomprehensible without a walkthru - but then again, many of these are that even with guides. :p
Beneath a Steel Sky (free) - Short and sweet with a great story.
All Monkey Island games - This should be pretty obvious. :p
Maniac Mansion & Day of the Tentacle - as are these.
Vampyre Story - this is a pretty new release, and from what I've gathered, pretty good as well.
for starters.
Strategy Games:
Warcraft 3 and Starcraft - the most popular RTS games on the PC. Anyone has to at least try these.
Command & Conquer- the First Decade: If you're into RTS games at all, you have to play at least a single C&C game, period. And with this one, you get the best of them in a single box.
Total Annihilation & Supreme Commander - Anything RTS made by Chris Taylor is good, period.
Heroes of Might and Magic 3 - Arguable the best game in the series, and still a great game - even though 5 is pretty damn good as well.
Emperor: Battle for Dune - somewhat more obscure than the above examples, so might be a little hard to get, but worth the trouble in my book: Non-linear campaign, three varied sides, and Michael Dorn. And it's Dune.
Warhammer 40K: Dawn of War - one of the best strategy games that isn't made by Westwood or Blizzard. Just don't get the Soulstorm expansion pack, it really kills the game in terms of balance and playability.
Turn-based:
X-com: UFO Defence and Apocalypse, Jagged Alliance 1 & 2, Warhammer 40K: Chaos Gate: These are the best Squad-based strategy games made. Pick one or all, you can't really go wrong with any of these.
...
Phew. I'll add more suggestions when I can think of them.
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