It depends on your application and data. We are using MySQL. When Oracle released a free developers version a few years ago we decided to test it just for fun. It didn't work out of the box, but none of the problems could be blamed on Hibernate. Below are a few of the problems we discovered. I am not 100% sure which version of Oracle we tested, but I think it was 10g express edition. I have no idea if the problems are still there in the latest Oracle version.
* Oracle convert emtpy strings to null. This was a problem in a case were we tried to insert an empty string to a column that was "NOT NULL".
* SELECT DISTINCT fails if there are CLOB column in the select statment. HQL queries that use Query.list()/Query.scroll() need to use Query.iterate() instead.
* We had an issue with a table name that was too long. It seemed like Oracle could not have names longer than 30 characters.
* In some places we bypassed Hibernate/HQL and used SQL with LEFT JOIN, etc. This didn't work in Oracle which needed theta-style joins instead.
We got as far as designing a few ideas for how to solve most of the problems, but in the end we decided to drop Oracle since it was just a side-track and no one had asked us to support Oracle in the first place.
So, I guess it is hard to say what problems you will encounter. The only way to know is to try it and see what happens. We had a bunch of test programs that we found very useful.