I grew up with Friends, but I never outgrew it. Not that the characters ever looked remotely older, of course (Jennifer Aniston dropped 20 pounds over the course of the decade, and became transformed from a rather dumpy, black-stockinged puppy into a svelte, polished best-inshow), but they did evolve.
They had to. Phoebe got married, Monica and Chandler adopted a baby, Rachel discovered a career and became a rather improbable and absentee mother.