I have a partitioned hard drive. I am running out of space on my main C drive, so I'm going to star moving file over to my D drive. I have a question though. Can I move the documents, music, video, etc folders too or will that mess up the system.

It depends on:
1) What the purpose of the D: drive is. If it's your recovery partition, you risk corrupting the recovery data (and the ability to recover your PC in the event of disaster) if you modify the data there.
2) If you move the files & folders using the Properties → Location tab → Move button everything should move flawlessly.