The responses on this thread have really surprised me!
I'm in my twenties, so I remember very clearly being sixteen. In fact, at sixteen, I was already dating Dh. I started college on a full scholarship at 17, and was really living a pretty fully "adult" life (complete with a great relationship with my parents) from that point onward. Without question, I was probably more mature than the average teenager (no sex before marriage, I didn't drink until I was married, blah blah), but really---
I would have been LIVID if my parents had tried to force a medical decision on me against my will at sixteen! I honestly can't think of much that would have made me feel more helpless and violated.
I have a lot of very strong opinions about medical issues. I'm anti-hormonal BCP, anti-gardasil, anti-lots of other mainstream stuff. Hopefully, by the time DD is 16, we will have a good enough relationship and will have talked about these issues enough that she will choose to involve me in medical decisions and/or make the decisions I would expect/hope her to make.
IMO, even 13 is very different than 16. This is clearly a gray area. If my 14 yo had cancer, and we had to decide between treatments, or something like that... I have no idea what I would do. I certainly HOPE that I would strongly consider the child's wishes and go along with them as much as possible (because, you know, there's always a possibility that the PARENT is wrong). I would certainly not be the first parent to force a child through incredible, futile suffering just because I can't stand the idea of losing him/her.
That, however, is very different than forcing a 16 yo to get a vaccine, or making her get a pap smear, etc, etc. I REALLY think that the most I would feel comfortable doing in that situation is saying, "DD, I feel strongly that you should do X, but it's your body, it's up to you."