It happens - the tail sticks out, after all, and can sometimes end up getting caught in or against something.
A fracture in the tail can sometimes cause mysterious hind end lameness - a lot of people forget to examine the tail. A horse with a broken tail may also hold it crooked. If not properly set, a broken tail may heal crooked, resulting in a permanently crooked tail. Otherwise, a broken tail generally heals fine - it's painful for the horse, but seldom causes any kind of long term impairment. In rare cases, the tail may have to be amputated. I've also heard of cases where the skin heals across the break and part of the tail is lost.
In some cases, the horse may, while the tail is healing, have problems lifting it to poo - resulting in manure in the tail hairs...in which case, the horse's handler may shave the tail. This can take weeks to grow back.