I managed to get Dungeon Keeper working under Windows XP. The great thing is that it also works with Deeper Dungeons (expansion pack) and with the Direct3D versions of the games, so here's the scoop:

1) HOW TO INSTALL:

Problem: if you try to install it directly, you will face an error message right from the start, mentioning it needs Windows 95, NT 4.0 or higher. The game does not recognize Windows XP as higher, so it will halt the installation.

Solution: in your Dungeon Keeper CD there is a folder called KEEPER. Inside that folder is another one called WINSETUP. You should run the setup.exe program that is inside that directory. It will prompt you to choose your language, English being the default, and it will take a while to allow you to click on next. It is faster if you are not running a lot of other things. When the computer is done "thinking", just click next. Installation will proceed as normal. If the computer keeps "thinking" for WAY too long time, kill the process with task manager and try again - shouldn't be necessary if you are patient though.

2) BEFORE PLAYING:

Problem: the game won't run directly if you don't patch it.

Solution: go to http://dk2.ea-europe.com/dk1/content/downloads/index.html and download the patch, the Direct3D updates and the fixed executables, and install them in that order.

3) HOW TO PLAY:

Problem: video runs and then the game exits to the desktop

Solution: right click on the executable files (keepd3d, deepd3d for the Direct3D versions) and choose "properties" then click the "compatibility" tab. Select the first option, Windows 95, as the compatibility setting. It should work fine now.

Enjoy!