Other than the paid gigs that I did lighting/sound tech for in the sixth form, I never had a paid job as a teenager. Unless you count the IT support I did for various people (usually for tokenistic reimbursement); the data entry type stuff I did in my Dad's lab on a couple of occasions mainly out of boredom (hanging around the lab was interesting enough); or the endless data wrangling and slide layout I'd end up doing whenever he was presenting at conferences because it was less painful than watching him fight the software.
You see, the problem was that growing up you're surrounded by people telling you to be sensible with money, and I was stupid and listened. I wasn't exactly rolling in cash, but since I had neither friends or a CD/substance habit, being sufficiently frugal with the inevitable annual gifts was enough to keep me in geek toys and books. I saw my brother get shitty cleaning and bar work jobs in order to pay for his frittering and underage smoking, and come home stinking of sweat and fags. Why get an exhausting menial job in order to pay for crap I didn't really need? So I didn't.
What nobody tells you is that you need experience of some shitty job as a teenager in order to bootstrap your slightly-less-shitty-job career path, until such a time as you're either a a shiny recent graduate in something employers care about, have accidentally developed enough of a reputation for competence that people start paying you to do things, or that you can rely on nepotism to get you a real job.
So yes. I'd say it's worth doing the odd crappy summer job here and there, but nobody's going to really care about how long you did it for, so don't turn down opportunities for real experiences in favour of them. It'll work out (or all go to shit) in the end regardless.