I think I was allowed to take the monorail around the resort loop (we were staying at the Poly at the time,) and I stopped in at each resort and browsed the gift shop, and rode back after a while, and I was probably about 15 or 16. Other than that, I never went off on my own (especially since the only other "kid" with me was my sister, who is a few years younger than me.) I would have felt a little lonely, and while I did consider getting off the monorail at the MK stop and going to the MK alone, I ultimately decided that I'd rather be there with my family anyways.
That said, if there's more than one teen and they've got a cell phone and they're required to check in from time to time, I don't think letting them go off for a couple hours alone would be too risky - as long as it was during the day, they are responsible, and that they stay where they are supposed to (I have a friend who had a BIG problem keeping her teenage brother from hopping on the WDW buses and going wherever he pleased without telling anyone!)
Of course, as someone already said, if it's going to stress you out a LOT to let them go off on their own, then it's not worth it. After all, this is WDW we're talking about, so it's not like they are going to be the only teens travelling with their family, so they likely won't feel like they're being treated like babies if you do want them to stick with you.
Happy planning! :wave: