Whether you "need" one is going to vary a lot on your tank, goals, feeding, etc. The short answer is you can have a great tank with or without a skimmer so "need" is probably not correct most of the time.
The two primary benefits in my opinion are gas exchange(again depending on setup whether you "need" it is another question) and removing organics before they breakdown to NP(ie keeping nutrients lower...again this may or may not be a benefit).
A third benefit in my opinion is helping me raise PH(hooking intake to an outside air line in my case or some use co2 scrubber).