I still have my original disks, and last year I installed them both with the official/unofficial patches and HR patch in anticipation for Fallout 3.
Unfortunately they both crashed to desktop so much and had the screen covered with blue goo you had to clear off with your cursor. Id buy a working copy in a second, but I just want to make sure im not burning 10 bucks from someone who has purchased from GoG. I have windows 7, Geforce 9800

As far as I know it works perfectly...I even play under Linux using Wine so I guess it will be fully functional on a computer with XP/Vista, as they claim.
I also have the original disk but it was a pain to try and make it work under Linux so I bought this version.

http://www.gog.com/en/forum/Fallout_Series/windows_7
One post below this.

Fallout 1/2 require you to check every box in file properties. That includes run in 256-color mode. And try running it in Win95 compatibility.

Gotta say, I bought it, patched it, and have only had two CTDs, neither of which I could repeat. Pretty stable release of a game that used to make me scream.
Next up is Arcanum...

I also have the original big box versions of Fallout 1 and 2 and have not had a problem with the DOS version playing in DOSBox, or a small amount of playing in XP SP3 with VDMSound and compatibility in 98. I have only played both, from the get-go with mods and patches though.
Gotta say, I bought it, patched it, and have only had two CTDs, neither of which I could repeat. Pretty stable release of a game that used to make me scream.
Next up is Arcanum...
See my post above - I have also not had a problem with Arcanum running on my XP machine, albeit never starting it without mods/patches from the get-go.
(had to post this way as site says 'original post doesn't exist when I try to reply!)