The main repository
Download the latest release or search for it on Maven Central.
Documentation for the OWL API is available in the wiki.
Javadoc for version 5 is available here.
Javadoc for version 4 is available here.
Javadoc for version 3 is available here.
Version 5 is the newest OWLAPI branch. it requires Java 8 - this means that additions to existing interfaces are much easier than it used to be in version 4. So, if you are irked by some parts of the current design and wish to have your pain eased, you are welcome to propose changes: fill in an issue or email the list with your proposal. Or, implement the change you would like to see in the API and issue a pull request.
Version 4 is currently used by tools like Protege, so it will be supported until the community moves over to newer versions.