This company offers overnight ferries from Barcelona.
http://www.balearia.com/
Costs from 38Euros for a single. You might like to sail one way and fly the other.
Here's another company that offer the service
http://www.trasmediterranea.es/trasm...di.do?codidi=2
There certainly used to be high speed Catamaran links between Alicante and Ibiza (Accion Transmediterranea used to offer a service that took 1 hour 50 minutes) but that doesn't seem to run anymore. High speed services should still run from Denia.