I went the Friday (late night)-Tuesday after Thanksgiving in 2011 and didn't find it bad at all...crowds weren't SMALL on Friday night through Sunday, and I wouldn't be surprised if Friday was a bit crazy (I wasn't in the parks that long).
But crowds weren't oppressive to me, not in the least. The only unusually long lines I found were for Pirates of the Caribbean, which had just come off of a lengthy refurbishment. Sunday evening was almost dead in the parks. Also, my mom was using an ECV to travel from land to land throughout our trip (she didn't enter the parks on Friday). We did not have trouble navigating, which shows that the walkways were not terribly congested either. The parks never hit capacity at all.
Many, many people have previously reported that the days BEFORE Thanksgiving are worse than the days after. I'm a bit confused as to why everyone is now saying that the days after Thanksgiving are absolutely awful.
I have a
wait board picture from I
believe 1 PM (and if not, it was 2 PM!) the Saturday after Thanksgiving 2011. It shows 10 minutes for BTMRR, 35 for Indiana Jones I believe, 25 for Finding Nemo Subs, and 15 for Small World holiday. The headliners like Space Mountain, Splash Mountain, and Star Tours were all under an hour. That's not
low crowds, but I've seen much, much worse.
Admittedly, 2012 could be very different from 2011 because a lot more non-AP-holders could be visiting the
Disneyland resort during this holiday period due to Cars Land. And those people without APs may be looking at past reports saying the days after Thanksgiving aren't that bad and making their decision based on that, which will in turn make those days crowded!
So we can't assume that the days after Thanksgiving 2012 will be OK...but in 2011, I did not think crowds were bad at all on the Saturday and Sunday after Thanksgiving.
And the week after Thanksgiving is widely reported to be low crowds (I found that to be the case the Monday after Thanksgiving 2011). Also short hours, though (I believe it was 9-8 when we went).