No longterm dangers other than for those with allergies. Ian Thorpe, one of the greatest swimmers in history, has a chlorine allergy, BTW, so it's not a deal breaker.
If you swim enough, you can start to lose hair on your head, eyebrows, etc. Nothing permanent, it will just start to fall out. Especially if you're wearing a cap, it will rip some out. But this will probably not be a problem if you just started, because this sort of thing doesn't start to happen until you're in the water 15-20 hours a week.
For those that might be having problems with dry skin/hair/eyebrows falling out, try vasoline!
Don't forget about the risk of swimmer's ear. Check out my article on preventing swimmer's ear at
www.swimcoachtools.com/BradenKSwimmersEar.aspx. Not directly related to the chlorine, but is a problem with pools.