The short answer is: weekend before crowds are light to moderate, then they build steadily toward Thursday. We did a lot even though the crowds were building by Tues & full blown on Wed. But we used FP and EMH strategies. However, our kids are older now, so our days of character autographs, Fantasy Land rides, & Toon town, etc. are over (sniff, sniff!). We focused mainly on the big thrill rides.
Edited to add: Many schools in Louisiana are off the whole week of Thanksgiving. We saw a lot of Saints & LSU hats, shirts, etc. around.
Here's the long answer listing what we were able to do:
We checked in the dolphin Sat evening late. Went to Boardwalk/ESPN club.
Sunday - We did epcot first then afternoon in MK for EMH. Got a FP for TT, then waited 1 hr for Soaring, then before doing TT, got another FP for MS! Got to MK @3:30ish, rode WDWRR to Frontierland, got FP for BTMRR, did POTC, JC, HM, then ate by 8 pm. then did IASW, race cars, COP, SM, TTA - done by 11.
Monday - AK early - Got EE FP (but had to wait until 12:15!) then did Dinosaur. Half did Kili.Safaris and Half did Lion King Show. Then on to EE! (Not much else we wanted to see, except for Nemo show, but line was horribly long!) Then MGM @ 2 for evening EMH - Did RR, got FP for TOT, did Backlot tour, Star Tours, Beauty & Beast Show, ate at Sci Fi, Movie Ride, walked thru Osborne Lights (beautiful!)
Tuesday - Epcot early - Walked onto Soarin', got a FP for TT, went back to MK for WDWRR, POTC, Pirate Tutorial (Which if you have pirate fans I HIGHLY RECOMMEND!!!), TTA, High School Musical show, Main St. shopping, Splash Mountain, lunch at pecos bill. then back to Epcot for Universe of Energy & TT, then Walked around WS: got FP for Maelstrom, then ate at San Angel cantina, did Maelstrom, then walked around countries. We didn't do the films. Watched Illuminations.
Wednesday - went to MGM walked into Stunt Show at 10:30, ate at Pizza Planet, then back to Epcot for Seas with Nemo & Turtle Talk with Crush (new & highly recommended!), ate dinner at French cafe (creme brulee' yummy!) left for home!