Don't overstay your welcome. Having a short, loved career will make you viewed as one of the better ones.

I don't think Eccelston ever gave an exact reason, but if you listen to the David Tennant Nerdist Podcast episode, he explains that Russell T Davies was leaving as head writer, and he felt it was right to leave when he did. He said he almost stayed when Stephen Moffat was chosen as the new head writer (since he wrote the best episodes, The Empty Child, Blink, etc) but he felt his time was done.

I think he said that if he stuck around any longer he'd never want to leave and wanted to end on a good note before people got sick of him as the Doctor (not like that would EVER happen but I digress). Also apparently he's coming back to do the 50th :D

God I hope that is true. I know they somehow had three of the Doctor's together in the 70s, so I would love to have the three latest together.

I think they actually had five Doctors together in another serial as well, it'd be awesome if they could get some of the classic doctors to be in the anniversary!

Eccelston said it was politics, basically..