We went Thanksgiving 2005 and it was great! The crowds weren't terrible- not even close to the summer months. We were there Saturday - Saturday. Thursday & Friday were more crowed than earlier in the week, but still ok. We did everything we wanted without a lot of waiting. Fast passes worked well for us on the more popular rides. I would definitely go during Thanksgiving again.
One note from experience- we went to MGM on Thursday and it felt pretty crowded. I believe that was due to MGM being smaller than Epcot & MK. If we go back during Thanksgiving again, we will do MGM earlier in the week.