To do something with all this computing power
After finishing the RC5-56 and RC5-64 contests, it was a natural next step because the existing client code base could be very easily converted to run RC5-72. Instead of making a mad rush to push the next generation, general purpose clients out the door, we decided to make the small alterations necessary to allow the existing clients to participate in the 72-bit contest as soon as possible. Providing new client software quickly helped maintain the interest of our large number of volunteers by providing a task we could continue to work on as a group.

To prove that small-bitsize encryption is insufficient
A loosely organized group of people on the internet (us!) deciphered an encrypted message in their spare time. That might be sufficient reason for the governments, security firms, and others to rethink their current beliefs of what "safe" encryption bitsizes are. Decrypting progressively larger bitsizes can only strengthen that argument by pushing the boundaries of what key lengths are considered feasible.

To explore the feasibility of cooperative networked multiprocessing
It's fascinating to see how easy (and difficult) it has been to band together this many computers, with this many operating systems, in so many time zones and put them all to work on a common computing task.

Because it's fun
Perhaps in the same way that writing a tic-tac-toe program in sendmail.cf is fun to some people, it's been a rewarding diversion for everyone involved.

Because you can win money!
There is a 10,000 dollar (U.S.) prize for the winner of this contest. After winning the RC5-56 contest we gave $1,000 to the owner of the computer that actually found the winning key, we kept $1,000 for ourselves and we donated the remaining $8,000 to Project Gutenberg. The prize distribution for this contest will be similar, and everyone participating has a chance to vote on which nonprofit should receive the majority of the funds. You can read more about the prize money distribution on the stats site. Other monetary prizes were similarly awarded for the completion of RC5-64, CSC, DES-II-1, DES-II-2, and DES-III

To get to know more people
You'd be amazed at the number of people you can meet by participating in this project, especially if you hang out in the #distributed channel on IRC, or subscribe to the mailing lists.

To attract the opposite sex
Well, maybe it has, maybe it hasn't. You never know ;).