I've used Hibernate (JPA implementation) and JPOX (JDO implementation) in the same project. JPOX worked ok, but ran into bugs fairly quickly, there where some Java 5 language features it did not support at the time. It had problems playing nice with XA transactions. I was generating the database schema from the JDO objects. It wanted to connect to a database every time which is annoying if your Oracle connection happens not be working.
We then switched to Hibernate. We toyed around with just using pure JPA for awhile, but we needed to use some of the Hibernate specific features to do the mapping. Running the same code on multiple databases is very easy. Hibernate seems to cache objects aggressively or just have strange caching behavior at times. There are a few DDL constructs Hibernate can not handle and so they are defined in an additional file that is run to initialize the database. When I've run into a Hibernate problem there are often many people that have run into the same problem which makes googling for solutions easier. Finally, Hibernate seems to be well designed and reliable.
Some other responders have suggested just using SQL. The real killer use case for object relational mapping is testing and development. The databases that are built to handle large volumes of data are typically expensive and or they are difficult to install. They are difficult to test with. There are plenty of in-memory Java databases that can be used to test with, but are typically useless for production. Being able to use a real, but limited database, will increase development productivity and code reliability.