I was wondering if this websites games are legit, and have permission of some sorts from the developers to sell these games.

That's a valid concern, but like Judas said, this site is completely legitimate.

Thanks for the answer. Now i'm going to go buy Descent 1 and 2, which are two of my most favorite games.

Well, I think it would be useful to highlight the difference with some abstract like "GOG... the legit abandonware alternative" :-P

too legit..
too legit to quit..

I have to admit that I was a wee bit suspicious to begin with. No DRM, low prices, high compatibility... it's like a textbook example of "too good to be true" but I've had fallout 1 for a week now and I've not been raided by the cops yet...

I was suspicious too, but after seeing GOG mentioned on sites like gamespot and other legit gamesites, as well as finding out their ties to The Witcher, seems they're legit.

Yeah, I think the site does suffer a bit from too-good-to-be-true syndrome.
But I decided to buy Fallout, 'cause I figure if I do get screwed, $6 isn't much, and everything works great, so I'm going to continue to support it, because this should be the direction digital distribution heads in.

I wasn't suspicious after I was allowed in the beta.

Well I wasn't suspicious for the legitimacy of GOG's rights to sell the titles they sell, but I was (and still a bit am) suspicious of the sources of the files they distribute.
I know that the only real difference between a pirated game and a digitally purchased one can be is the source of the download and can be impossible to distinguish, but there were already two cases of GOG games where some movies were missing. Movies that were included on the original game CDs back in the day. Missing movies/music/speech was very common with pirated CD-rips back in the 56k days as downloads needed to be kept as small as possible. I think you see where I'm going with this.
Also some of the manuals on GOG have the replacementdocs watermark...
Again: I'm not doubting the validity of GOG's right to sell those files, just the source of the files themselves.

I would think they get them from the developer/publishers themselves, as they negotiate with them anyways, so it's no deal to give them the game/source.
Why would they look for a pirated version when they officially are allowed to sell it? And that they got rid of every single copy including masters etc at the publisher/developer..it's rather unlikely i would say.
Also it isn't like the games wheren't available anywhere for 10 years and now mysteriously appeared on GOG, most of them are still for sale at other places, like budget bundles at your local store or at Amazon etc.

Actually, you'd be surprised how often stuff gets lost. Especially the source code used to remain with the developers and since many old companies don't exist anymore, the only place where you can find it is often the original programmer's machine. And if that one goes belly up, the code is often lost forever. Heck, if the original data was usually still available, then half the commercial emulators (I mean the one developed by SEGA, Sony, Microsoft and pretty much any other company which has done business with software for more than five years) wouldn't exist.
Of course, a handbook is usually easier to find :)
Interesting sidenote: Can an illegal derivative have a copyright of its own? For example a CD cover, made partially from copyrighted images.

I think in that case you could only claim copyright for your specific modification of copyrighted material rather than on the original. If someone else tries to pass your modification off as their own, you could sue them but if they rearranged it then the only person they're ripping off is the original creator.
Of course once the lawyers find out that you've been using copyrighted material you might both be meeting your future husband in prison...