My first GOG was Soldiers: Heroes of World War II.. And no, yet to finish it.
Though I owned the retail, it might not count?
So... Ghost Master, and no.
(yes, I am ashamed at my apparent spending addiction)

Uuu, thanks! Apparently, it was MDK 2 - and I have never really finished it.

Fallout was my first purchase.

Giants: Citizen Kabuto with a free copy of MDK. Completed both of them, very fun action games.

See, GOG hasn't got OPF, not yet anyway.

It did have it but for reasons I can't recall it was removed form the catalog.

Yes, they did have it, though it got removed because the publisher got too bitchy about something.

My first buy was the Jagged Alliance series, Fallout and Conquest of the New World. Kept me occupied for a while :)

Really? Huh, that's something. How does that go for the buyers?

I assume the game's still on GoG's servers, just not for sale.
As for my first game, it was UT2k4. Then I downloaded Beneath a Steel Sky, then that Mean Streets game. The I bought nothing new for a long time. Then came Outcast, which I think was a day-one buy for some reason. Few days later, after talking with a friend of mine, I was persuaded to buy Giants: Citizen Kabuto. A few days ago I found a disc with Freespace 2 OEM (10-mission demo) on it. Loved it, bought the full version from GoG.
And for some reason, I just told you my whole gog-story.

The first two Fallouts, along with the freebies later on. Haven't yet completed any...
However, nothing can compare the orgasms that ensued when HoMMIII came along. God, I played it furiously for a week. So good.
And then the Myst series, Sanitarium, Phantasmagoria, BG&E... Oh, the wonders... :')

Fallout, like a lot of people I bet.
Been a great service since then!

The trio of Operation Flashpoint, Fallout Tactics and Giants : Citizen Kabuto.

So far it has gone very well. I can still download ToCA3 and Colin McRae 2005, I assume that those that bought Operation Flashpoint still has access to it as well..

Atypical games for me : Patrician 3 and Port Royale II.