Okay, I know this isn't "new" Doctor Who, but I figure you guys will forgive me.
I just rented "The Five Doctors" (made in the early '80s) and watched it with my daughter. Have you guys ever seen that special? It's with the "original" 5 Doctors. After we watched it, we wondered why Tom Baker (Doctor 4) was hardly in it at all. Afterwards, we took a look at some Who's Who stuff, as it were, on the DVD, and discovered that Tom Baker had declined to participate in the movie. Anyone know why? They only showed archival footage of him in the special.
The other thing we thought was interesting was that the actor who played the first Doctor died shortly after "The Three Doctors" special aired and they had another actor portray him in "The Five Doctors", though the fellow looked so similar to the original actor, we had assumed the differences were due to aging. Interestingly, that actor died shortly after the making of the special, too.
In any case, if anyone knows why Tom Baker didn't want to participate in that special, I'd love to know. He was the Doctor I grew up with as a teen.