Hibernate doesn't need anything other than a database, a JDBC driver, and a JVM.
My website has a variety of examples, most of which can be run and tested simply from the command line of a JDK (check out my signature links for more info). That's part of the beauty of Hibernate.
To run as a web app, it's as simple as putting the Hibernate jar files in the lib directory of the web applications. That will provide design time linking and deployment linking, although there are other, perhaps more layered strategies, for application packaging. I always run Tomcat as a test server with my Hibernate applications, even if the target environment is WebSphere or WebLogic.
Of course, anything that can run hands free on a JVM can also easily be integrated into web based or J2EE/JEE5 based applications. And as such, you see plenty of web based applications that leverage Hibernate as an ORM tool. But again, it's certainly not needed.