There are a couple of options. Oracle SQL Developer has a built-in test suite but that's no use for people using other IDEs such as PL/SQL Developer, and also not helpful for CI purposes.
The best choice is UTPLSQL, which was originally written by the renowned Steven Feuerstein. This is pure PL/SQL. It is pretty good and free open source software.
The really good news is that - after a long period of hibernation - UTPLSQL is back in active support. Version three is a complete re-write, with clever support for readable tests: it's a lot more like the JUnit and NUnit style of unit testing. Excitingly there are hooks for running UTPLSQL tests - including rendered output - in CI tools like TeamCity, Jenkins, etc. There is also a community of developers writing helpful extensions, such as a SQL Developer plugin.
There's a migration tool for v2 tests.
Author's note: I have completely re-written this answer to reflect the fact that UTPLSQL is now an active product again.