What to do with a cluster of old computers running Ubuntu?

Put some sort of distributed computing client on there and donate your unused cycles to science.

Maybe something like http://folding.stanford.edu/

If the computers have a reasonable network connection, there are a number of services you can run to make the internet a better place. Few of the things I'm about to list are directly parallelizable across a cluster, but many of them work very well when used on a pool of machines with a DNS round-robin to load-balance and reduce the impact if any one of the machines goes down. In addition, you can perform maintenance on one machine at a time, while leaving the cluster and the services unaffected.

• run a network time daemon and add it to the time server pool
• run a GPG keyserver and add it to the keyservers pools
• run a Tor bridge or relay, and mirror the Tor Project website
• run a Mixmaster email mix server
• run a Convergence or Perspectives notary to keep track of SSL irregularities
• run a full instance of the SSL Observatory
• run a Tahoe-LAFS node to participate in a secure, distributed filesystem
• run an I2P or GNUnet node

The great thing is that most of these services aren't very processor-intensive, so they run really well even on older hardware. For these sorts of services, it's less important how much total processing-power you can contribute, and more important that there's a diverse set of machines involved. That's why I'm recommending them rather than contributing to one of the many @home projects:

for an older machine, you get a lot more make the world a better place with these sorts of services, than something which just wants all the CPU it can get.

Of course, with your leftover CPU time, you can still try to cure cancer or search the skies.

You may try mining some bitcoins. This virtual currency based on peer-to-peer protocol (and which can be easily exchanged for real money, at the moment of writing a bitcoin is worth about $11) has coins, which are generated not by a single institution, but by the network of all its users. The chances of having generated some amount of such money are the greater the more computing power you have. When you will have started, you can calculate if it will pay off.