I am currently working on a rather large project, and I have used JUnit and EasyMock to fairly extensively unit test functionality. I am now interested in what other types of testing I should worry about. As a developer is it my responsibility to worry about things like functional, or regression testing? Is there a good way to integrate these in a useable way in tools such as Maven/Ant/Gradle?  Are these better suited for a Tester or BA? Are there other useful types of testing that I am missing?
It is your responsibility to strive to deliver defect-free code. You should write, help write, or ensure tests get written or performed in order to give you confidence in the code you are delivering. 

Note: I'm not saying you are required to deliver defect-free code. Rather, you should attempt to write the best code you can for the requirements you were given. Part of being able to do that means the code should be tested. 

Whether that means you are personally responsible for functional and regression tests is mostly a function of how your company is organized. All of the highest skilled programmers I know don't ask themselves "is it my responsibility to write tests of type X?". Instead, they ask themselves "what must I do to make sure my code is properly tested?". The answer might be to write unit tests, or to add tests to the regression, or it might mean to talk to a QA professional and help them understand what tests need to be written. In all cases, however, it means that they care enough about the code they are writing to make sure it is properly tested. 

Bottom line: you should be responsible for delivering high quality code. If that means you need to write some functional or regression tests, do it.
