Star Trek: Voyager
Admittedly, The Doctor could get a little full of himself. Most amusingly, this was demonstrated in "Author, Author" when the crew rewrote his holonovel Photons Be Free! to paint him in the worst light after the original version had everyone else look bad (the rest of the episode takes things more seriously, rest assured, but this is one of those instances where the old joke, "It hurts when I do this"/"Then stop doing it!" is once again hilarious).
"Virtuoso" is another such experience. The nature of this medical emergency is an alien civilization that has never heard singing before. The Doctor sings for them, they fall in love, he thinks it's a brilliant idea to leave Voyager behind and pursue this exciting new career, and of course he ends up proved absolutely wrong.
Not one of the best Doctor episodes, but certainly captures the character in a nutshell.