I felt like playing some PC games since I never got into it very much so far. While i've played some games, almost none to completion, consider me a blank slate. I'm looking to play adventure games and RPGs mostly. Don't recommend any RTS as I'm not in the mood to get into them right now. Same with FPS, not interested. The only two I'm looking to play are System Shock 1 and 2 so let me know if it's worth going back to these games and playing them. Remember I will have no nostalgia factor with most of these games, so try to aim for games that have aged well. For instance, I'm starting with Fallout, so no need to recommend that series to me. Also try to give me the year your picks came out if you can, because I'm not looking to play anything current as in the last 4-5 years.

Star wars kotor. Its a little old now but was an awesome game that also came out on xbox.

Baldur's Gate I (1998) & Baldur's Gate II (2000) and expansions for both. Epic stuff.

http://en.wikipedia.org/wiki/Baldur's_Gate_series

Icewind Dale I (2000 ) & II and their expansions are similar to Baldur's gate in every other aspect apart from them being more hack and slash whereas BG is more story driven.

http://en.wikipedia.org/wiki/Icewind_Dale_%28series%29

System Shock may be a little old if you're not used to old DOS games. If you're quite new to PC gaming, you could try Fable which is really a hybrid console/PC RPG or the Witcher if your PC handles it.
Baldur's Gates 1&2 have maybe the best storytelling among PC RPG.

Otherwise I would suggest not to limit yourself to RPG/Adventure Games since a lot of unique games came out on PC.
Trackmania Nations: free online racing game
Portal: First Person Puzzle
Heroes of Might and Magic: Turn based fantasy strategy game; very relaxing and addictive. Try HOMM3, its a classic.
SWAT4: Tactical Squad FPS where you almost never shoot
Racing games: The best simulations are on PC (Richard Burns Rally, F1 Challenge 99-02 (old but good), GTR2, rFactor (a bit hardcore))

Play Portal, its good.

Thanks for the suggestions so far guys. The reasons I had to limit what to recommend was because for one I'm not too interested in genres like simulation racing and some other mentioned. Secondly, I asked for games 4-5 years old because I don't want to have to worry about being able to handle the game. I don't have a PC that's set-up for current gaming. Thirdly, try not to recommend me games I can play on consoles. I'm looking for PC exclusives. I already have a 360, PS2 and Wii to play games like Portal, Fable and KOTOR on.

Arcanum, wonderful game in a wonderful setting with wonderful music!

Adventure Games:
Portal
Indigo Prophecy
The Longest Journey & Dreamfall
Grim Fandango
Myst Masterpiece Edition

RPGs:
The Elder Scrolls IV: Oblivion & Shivering Isles
Star Wars: Knights of the Old Republic 1 & 2
Planescape: Torment
Baldur's Gate 1 & 2

Series are listed from newest to oldest. In my opinion, the games that show their age most are Baldur's Gate 1 & 2, Planescape: Torment, and Myst. But all are still great.

Grab SCUMMVM and play Lucasarts classic adventure games:
Day of the Tentacle, Monkey Island 1&2...

Hack&Slash: Diablo 2 and Sacred

Sid Meier's Civilization 4 it's a great Turn Based Strategy game but it might take to much time for you.