I liked being 18 and 19 best, I absolutely hated 13-15, and 16-17 were merely alright.
Being a teenager is an exciting time because you're old enough to be able to think critically/process 'big' ideas, but you're not old enough to realize that these ideas aren't exactly essential to your needs/new to anyone else. People are more impressed by you, and you mostly don't realize that it's actually because their expectations are lower… and they give you a lot more slack. There's still time to make the big decisions about yourself, and people don't judge you in terms of your socioeconomic standing (well, they do, but all of your peers are students and therefore still mostly equal). You can also abuse your body (in terms of drugs/alcohol) a lot more and get away with it, because you heal faster and don't have to work as hard to look/feel healthy. Your parents get a lot more permissive in your later teens and even though you're living under their roof/their rules, it's not like you're a kid and you still do have a lot of freedom… and there's just so much that is exciting and new at that time. Oh yeah, and you probably look good as well… I do miss being cute.
Still, I think it's pretty far from being the prime of your life. For the most part, you still don't have so much control over what you do with yourself… you're stuck in school and even though learning isn't exactly torture, it still sucks because you don't have financial independence and you can't just do whatever you want. And if you're unpopular/bullied then it can be absolute hell, because there's nowhere to go and you don't have the means to escape.
I'd have to say the prime of life is probably late 20s early 30s, depending on whether you're working a decent job or not. Money IS freedom, and financial independence means that you can do pretty much anything you want, as long as its legal. Even the little things like eating whatever you want for dinner whenever you want, or going out for a run in the middle of the night, or not having to explain where you were, etc. are pretty awesome. It's harder to make friends, though… the whole socioeconomic boundaries thing is a pretty big deal, and people are more self-defined so they're less likely to have a lot of things in common.
But you get to spoil yourself with presents, donate to causes you care about, travel to other countries on your holidays, discover all kinds of new things about yourself, and best of all, you start improving yourself for the sake of improving yourself (as opposed to having someone TELL you to improve yourself unless you want to be a loser at life). I guess some people do that anyways, but I could never afford it until about 5 or 6 years ago-- it was either debt or something else.
I would say most of the people who reflect on their teenage years as the 'best years' are probably married with children and lamenting the loss of their independence.
I really do hope that the best years of my life are yet to come… I've had some ups and downs over the past little while but overall it has been much better than when I was growing up.