Eleven, Two and Five, each had very good exits when they regenerated. They're actually my top three (in that order). Eleven's speech about accepting change, but not forgetting the old, Two not going out without a fight when being judged by the Time Lords, and Five giving up his life just to save Peri in such a hopeless situation. Those were good exits for a Doctor.
For companions, that's a bit harder since they're so many of them, though I'd have to say Lucie Miller's final exit was the best. Seriously, she crashes a nuke into the Dalek's time engine, and blows them all up! The effect it has on the Doctor is just heart-wrenching, and him listening to her recording at the very end of that story...
There were some other good ones I liked. Jamie and Zoe, because of how cruel and sad it is and how it pushes Two for his final moments, Tegan, because things just became too violent and stopped being fun, and Martha, because she was able to move on with her life because Ten wouldn't.