There is a prestige playlist, which you have to have prestige'd at least once to enter. This isn't exactly a game play benefit, but you will theoretically be playing with better players.
Here are the current options on that playlist:
- Prestige TDM is unlocked right away.
- Prestige Hardcore is unlocked after going prestige 10 times.
- Prestige Pure is unlocked after going prestige 15 times.
As Aardvark said unlocking the all the custom classes can be particularly helpful if you want to run similar weapon sets but with different equipment. For example, starting a round with marathon+lightweight and you favorite weapon. Then after the initial points have been captured swapping to scavenger, warlord, and your favorite weapon.
And although this isn't exactly a game play benefit you can pay $50,000 after going prestige to unlock the prestige leader board. However, this is lost once you prestige again.
Lastly, there is the (laughable) intimidation factor (What do you mean no one cares?)