Why do professors take on service duties?
Most professors are required by their departments to do some sort of service to the university and department. It's a duty of their job, often assigned by their department chair, and may be required as part of their tenure case. Someone who is actually a professor may be able to say more. 

Paper reviewing, and the peer review system as a whole, is a cooperative system. Profs need peer-reviewed publications to get tenure, so someone has to do the reviewing. Nobody gets explicit points or credit for  reviewing, but if everyone tried to free-ride, then no papers would get reviewed, and the system would collapse. As a non-professor, I don't do as much reviewing (dozens of papers a year) as my professorial colleagues (hundreds per year, often, depending on field), but every time I submit an article to a journal, I'm asked to do a review by the editor, which helps keep me involved in reviewing. I suspect that people also don't want to develop reputations as free riders, so when asked to review, within reason, they do it. 

In addition, sitting on a program committee for a conference involves a lot of reviewing, and it can be a great way to meet and network more closely with more senior or more junior researchers depending on your own level, both of which have their advantages. Doing both kinds of reviewing and doing it well can help one build a reputation as someone who supports the system. Besides the general benefits of a good reputation, it may lead to program committee chair positions, other conference organizing positions, and journal editorships. 

In the end, having a bad reputation for not reviewing and not doing other kinds of service could seriously affect one's tenure case or future job prospects.