Bent pipes were very popular in the 19th and early 20th centuries, but from 1919 to 1940, their popularity waned. They made a comeback in the '50s and '60s, and are now as popular as they were a hundred years ago. Semi-bents, with less curve, are also popular.
Bent pipes are much easier to hold in your mouth and do not exert nearly as much leverage as a straight pipe.
They also allow the smoker to catch an occasional whiff of their own tobacco directly from the bowl.
Most people find them much easier to light and keep lit because you can see more of what your doing.