I, personally, feel that you only outgrow a show when it no longer has anything to offer you. Sesame Street, even in its current form, still offers me some laughs now and then, so I don't count it in the same camp as some other kids shows, which offer nothing to most people over the age of five (at least in my opinion). To give up on a show that still entertains you just because others have told you it's time for you to stop watching it, to me that's just peer pressure, which nobody should cave into for the wrong reasons (are there right reasons? I'm not sure, but I don't think so).
On the other hand, if you lose interest in a show and something else, perhaps another show, takes its place, then that's fine, by all means, don't stick with something just because you feel obliged to.
And I won't deny it, there was a time when I felt obliged to stick with watching Sesame Street every day. It still offered me some fun moments, but overall I was discovering other TV shows (among other things). I didn't "give up on it", because I still watched it occasionally (especially my library of episodes I have on tape), but if there wasn't a need to watch it every day, then I don't see why it's a bad thing to stop.
But to stop watching it altogether because someone tells you you're too old for it is like throwing away a perfectly good sweater that you like a lot, just because someone else has told you it's out of style. What's so wrong about hanging on to it?