Unwanted pregnancies.
Sexually transmitted diseases.
Apart from the excellent answers given by Hippy and Cookie, I can't think of a single thing. Sex is such a necessary part of life that celibacy (whether voluntary or compulsory) can have all manner of psychological side-effects.
On the other hand I really don't like the idea of indiscriminate coupling. There's surely gotta be more to it than that. Without affection, it's pure barnyard.