On my 2005 trip, I had two 14 year olds with me. They really enjoyed the character breakfast over at the Beach Club (Cape May buffet). The characters there are Goofy, Minnie, Pluto, Chip and Dale all dressed in beach/surfing attire.
Goofy, especially, seemed to ham it up real well with the teens and they didn't feel out of place at all. Also, the character breakfast here is always very low-key (i.e., not a lot of toddlers running around trying to hug the characters and coming up to YOUR table).
On the other hand, I will agree with the other poster about face characters. On this past trip, my kids were 15 and 12, and we happened to have dinner over at 1900 Park Fare (all we could get into). They have face characters there who, awkwardly, tried to pay attention to my older kids. Good for them, but it was kind of awkward because my kids feel weird with it. The face characters are definitely better for the young kid.