If used according to the directions on the box, there are no significant dangers. However, TSS is still a risk if you leave the tampon in for too long. It should be removed after 6 to 8 hours of use (depending on the brand).
Toxic shock syndrome is still a danger. They still have warnings on the papers inside of a tampon box. I think it is more of a danger than ever because of the absorbing ability of the new tampons. They hold a lot so women leave them in to long.