My recommendations for fantasy Strategy/RPG's are, if you like Turn Based combat: Temple of Elemental Evil + Circle of Eight patch, and if you prefer Real Time: Icewind Dale + Heart of Winter + Trials of the Luremaster & Icewind Dale 2.
I'm getting the impression you're more interested in RPGs than Strategy/RPGs (for example Jagged Alliance, Silent Storm, Freedom Force, Shining Force, etc). If that's the case, you can't beat Planescape: Torment for great plot and characters.
I also agree with most of the recommendations in this thread, particularly Fallout 1 & 2 and the Baldur's Gate series (wandering around dungeons fighting random creatures?!
fanboi rage... rising...) are must play games, and I'll add a potentially controversial personal favorite; Arcanum: Of Steamworks & Magick Obscura.
Vampire the Masquerade: Bloodlines, The Witcher and Deus Ex are also faves of mine. Leaving personal preferences aside, I think every game mentioned in the thread is at least worth a look (even... ugh... Fallout "3"... actually, screw Fallout 3, try New Vegas instead), and virtually all of them are available very cheap.
How far back are you willing to go? Have you played Sierra's Quest for Glory games? I can think of a lot of RPGs that you might enjoy, but I'd say they're at least a couple of notches below those already mentioned.
EDIT: D'oh. I walked off to make some tea mid-post and kuze beat me to the punch on PS:T and Arcanum.