Forgive me if this is GOG's trade secret, but I'm curious how old games are made compatible for modern Windows (XP and Vista). It seems to me like some reprogramming of the software is necessary. Does GOG actually do specific software modifications, or do they have some sort of nifty engine that can take old executables and run them in Windows. I know Windows has a "compatibility" mode... is that all we're using here?
I haven't purchased a game yet, so maybe that's why I'm in the dark.
Secondary question: GOG has to get the rights to "re-publish" these games, correct? I hope they can get the rights from LucasArts... most of my favorite old games are from that company.

For DOS games they are using DOSBox. For the Windows games, some normally work fine in XP/Vista. For the few that don't I have no clue, but its probably a slightly different solution for each game.

Cabal said it.
Some games on GOG will still work under XP and VISTA.
The really old DOS games that cant run on modern PCs come with a pre-configured copy of DosBox.
DosBox is an incredibly useful program that creates a simulated DOS environment under Windows that allows you play old DOS games. Think of it as a DOS emulator.

I would think that they would be recompiled. There may be some minor code changes. Nothing that would change the game, but just how it is executed and how the code is read by a modern OS.

Some games are using a frontend gog.exe, but I don't know how it works and what does it affect. Also, some registry entries can be found in local_machine, in the gog.com directory.

They have the source to some games, which makes fixes much easier - in some cases, trivial. Just recompiling with a more modern compiler and libraries may be enough.
For other games, the source is unavailable or simply no longer exists. In these cases, GOG do have the capability to reverse engineer the games, but this is much harder and I don't know how much effort they are willing to put into any one title.
Another problem they are likely to run into is the lack of GLIDE support in modern graphics cards. For this, a glide wrapper can provide a glide API and translate to either D3D or OpenGL which modern GPUs can understand.