My first game here was Beyond Good & Evil(i think it somehow also was the reason i found GOG) and since it is a pretty short, straight-forward but VERY captivating game, i finished it straight away

might and magic collection

Not counting the free ones that were available when I joined...
FlatOut
Neighbours from Hell Compilation
And yes, I've completed both.

Fallout 1 and 2 (got both for 1 price, a promotion for the beta of GOG). Haven't finished any of those (yet).

Duke Nukem Manhattan Project - ended in a middle?

My very first GOG purchase was MDK 1+2, followed by Giants: Citizen Kabuto two days later.
I finished MDK back when it was new, though not this time around. MDK 2 I've only played very little. I haven't finished Giants yet. I'm into the Kabuto missions, but other stuff came up, and I never got around to finishing it. Maybe I should do so soon.

That was a while ago, but I think my first was Arx Fatalis. If memory serves I was still a bit skeptical of GOG at the time, and thought it would be a good game to test out the service with as I knew the original version of the game tended to have problems with modern systems. Many games later I can say that it passed my test quite nicely.

My first was Gothic, I think. What a deal. :)

Excepting the two free ones that existed when I joined, the first ones I bought were Broken Sword 3 and Abe's Oddysee.
Of those four I have only finished Beneath a Steel Sky. I think, I don't remember if I only came near the end of Broken Sword 3 or actually finished it back when I played a pirate copy before I knew about GOG.
Go to your list of bought games, view it in list mode instead of shelf mode and it should display the games ordered from latest bought (top) to first bought (bottom).

Nice thread.
Fallout, and yeah, I beat it quite happily. My co-worker wouldnt shutup about it and I knew this new service had it for cheap so I gave it a shot. I remember being annoyed with it at first (this was the first game of its kind I'd played on PC)...clicking this or that wouldn't give me the results I wanted. But I figured it out after a couple hours, started over, loved it. When I got the leather jacket at the start I became addicted. :)
Character was a lady, master of hand to hand combat...real mean with the Power Fist.
I remember being amazed at all the free stuff that came with it, especially the Fallout bible.
Shortly after I got Fallout 2, then awhile after I guess the free GOGs got me back into it. Was addicted from there on.

Besides the three free games, my first buy was during the Kalypso discount:
Commandos Ammo Pack, Commandos 2+3, Tropico Reloaded, Patrician 1+2, Praetorians,
Imperial Glory and Port Royale, with a $25 discount. Not bad, huh?

First i grab the Free games to check out GoG's Handiwork, then i used a Promo Code that i got with a Magazine i subscribed to for my choice of Three Games - i chose Kingpin, then i got a Gift code for Tex Murphy Under a Killing Moon (Thanks to Interactive Distractions) and finally my First Purchase was the Prince of Persia Sands of Time and Beyond Good and Evil in the 2 For 1 Offer
No i Have not Yet Finished any of them, though i have completed some of my later Purchases before Getting them on GoG

My first was Operation Flashpoint. Good game, but I find it to be very difficult and I never made it all that far. I really should get into it again.

Freespace 2 with Descent 3 as my free game

Colin McRae Rally 2005 and Screamer (from a promotion with them both).
It took me forever but I finished CM. Screamer, on the other side, I couldn't finish.