I read through the stickies and FAQs and I apologize in advance if this is answered but I did not see it. I did see where we "own" the games we buy/download, but that is not the exact answer to my question.
I'm a new user here and finally posting after lurking for a month or so. The computer I usually use is a mac laptop with snow leopard OSX, although I have a PC with XP that is *not* connected to the internet. I would have to go buy a wireless router for it if my question is answered unfavorably.
Can I download a game to my mac, put the files on a flash drive, and move it to my PC where I know the games will work, or do I have to play the game on the computer it was downloaded on (like a Steam authentication system or similar function)?

Yes, you can download the games on one computer and move the installers to another computer. There is no DRM or internet check what so ever. It's like downloading and installing freeware games except you pay for them. You can even install them on all your own computers.
Just don't share the installers with anyone by any means as that would undermine GOG's whole business model and trust they place in you by not having DRM/athentication meansures in place. If too many people do that or GOG installers start appearing on torrent trackers or similar peer to peer distribution services, GOG will either go out of business or have to employ DRM to appease the devs and publishers here.

There are few older (90's) games that still have their copy protection in place due to them being integrated into game world itself (like guard at city gate asking copy protection question). For these GOG provides answer sheets. Also some multiplayer games require cd keys/serials for internet multiplayer. Those you can request from support as needed.
Oh and welcome to GOG. Hope you enjoy your stay. In case you don't know, there's Wishlist where you can vote for games that you wish to see in GOG. How effective that is, only GOG ;-) knows.