I use Hibernate together with MySQL 5.1.30.
I have the next libraries:
That's a pretty old version of Connector/J. To make sure you're not battling a known and fixed bug, I'd start by getting the newest one (5.0.8):
http://dev.mysql.com/downloads/connector/j/5.0.html
That EOFException from MysqlIO is a bit suspicious. Under normal/non-buggy usage, you shouldn't ever get errors from that layer.