There are a good number of games that I would choose if I did not already have a copy. Master of Orion 1&2, Divine Divinity, Sacred, the Realms of Arkania trilogy, the Might & Magic 6 pack, Icewind Dale, Ultima 4-6. That should keep you busy and drain your wallet surplus.
Thanks for all the suggestions, guys! I think I'm going to start with Master of Orion 1+2.
Let me add one suggestion that was e-mailed to me by Sphynx, for anyone else picking through this thread for suggestions: "But, if you are looking for a great game at GOG.com I highly recommend Advent Rising. The story alone is worth (penned by none other than best-selling sci fi author Orson Scott Card). I just thought you'd like to know."
And lets keep this going--I bet there are a lot of new Goggers out there willing to bet a few bucks on a new gaming experience!
Master of Orion II and Master of Magic are sure picks. Those old 90's SIMTEX games have a kinda of "Origin" feel to it, as they are very good games with a lot of soul. I played a lot of those two. Raptor: Call of the Shadows still holds its own as a shooter.
There is also Cannon Fodder,
I have been playing this one in the evenings if I need a break from work and the diffculty curve is still as astronomical as I remember. Its a quirky little game, with a fair amount of dark comedy in it.
Wait, WHAAAAAAAAAAT?? I-War is on GOG??? Oh, [insert deity], it's true! There is justice in the world. (Translate: I-War is awesome through and through. However, it's probably the most difficult game I've ever played. I think I could finish the training missions without invulnerability, but...)
I don't really go there very often (just went there to check up, and found that I suddenly had Ultima IV in my library, waiting to be downloaded - k, thx, not that I ordered it), but I can vouch for the quality of nearly all of their D&D-titles, if CRPG is your cup o' tea. Dark Reign is also the first and only strategy game I ever liked (1, not 2!) - can't say I know why, but it does seem to have brought some technical innovation to the RTS-meme. The story is, I suppose, not the main attraction.
I think the Myst and Uru games have their appeal, but Uru is perhaps just about to take off - Cyan fairly recently went official with their plans to opensource Uru. Perhaps a VERY niche series.
Also consider staying well away from Syberia. I suppose they're solid adventure games, as the games themselves go, but the stories are just... w3rd. Cute tales of misfits/outcasts/outsiders/progressives looking for a purpose in life, I suppose, but... w3rd. Weirder... W333333333RD!