For all SCUMM games use ScummVM.
If you are experiencing problems with cutscene playback in CMI go here
If you are having problems with EMI (Monkey Island 4) get the patch
. If this does not correct your problem then try running in Direct3D rather than OpenGL mode or vice versa (configuration options, troubleshooting tab).
If various LEC games insist on trying to install an old version of directx before they will run (then failing and not running) try creating a blank .txt file, naming it DDHELP.EXE and placing it in the windows/system32/ folder.
If you have problems running the CMI demo in WindowsXP run it through ScummVM.
If you have problems with Grim Fandango see here
or the post below for a general overview of the things you can do with GF that *may* help you get it to run. Try the patch
first of course.
Finally theres the Lucasarts support
page. You might be able to solve your problem there. If you do, remember to look out for flying pigs.