... https://www.youtube.com/watch?v=BehwuPQm16A"]The Eleventh Doctor Regenerates... The Twelfth Doctor Appears! - Doctor Who: Christmas Special - BBC - YouTube
Great episode! Didn't think I'd be as emotional as I was but Smith did a brilliant job! Tennant's regeneration still hits me the hardest, but Smith's is pretty close now. Having Amy come back for those few seconds was brilliant!
Most of the time the reasons boil down to either the actor wanting to move on and pursue other things. OR Sometimes if a Doctor has been around for a while, they'll 'refresh' the show by adding a 'new Doctor'.