The first and only "relationship" I've ever been in had this sort of problem...
When I first met her in person, I was 17, and it was her 34th birthday.
I'll spare everyone from getting too detailed on why/how this happened and how it played out; but long story short, although we got along very well, it became very evident that the two of us were just in such different stages of life that trying to pursue said relationship just wouldn't work out. I was (and arguably, still am) in a stage of life where I was still feeling too dependent, too ill-prepared, too incapable, too scared of the outside world... she was at a stage of life where she wanted to settle down, start a family, all that jazz.
The whole experience was a big eye-opener for me and it taught me much. While our "breakup" was hard on me, as they tend to be, today I don't regret what happened at all. If I got to do it all over again, I would. That's how valuable the experience was to me.
One question that frequently came up in my mind both before our meeting and after the fact was whether age really was just a number. Today, I still believe that it is. Bottom line -- we are essentially MADE to be able to affect and be affected by one another. Age doesn't really matter in that. However, it's more likely that two people with distinct age differences are going to be in two different stages of life -- and THAT kind of thing, while it may not be as problematic for something like a friendship, it might be so for a relationship.
In the end though, it depends. Some teenagers are spoiled brats, some of them have such maturity that you might find yourself shocked at how young they really are. People are all different, but then again, that is what keeps us interesting.