Best answer as chosen by user rbspot: What I would do . . .
If you simply move the "My Documents" folder to the other drive you may hose up any links to that folder. What I would do is find specifically what I wanted to move such as pictures, files, documents, etc. and then drag and drop to the D: drive.
Then, again, it may not be specific files that are filling up the C: drive. Installed programs could be the culprit. If this is the case you would need to uninstall them and reinstall them on the D: drive. The down side to this is that most programs will not install on any drive other than C:.