Keep in mind the difference between unit testing and integration testing.
Unit tests should be testing code without any outside dependencies. These dependencies are mocked using a framework like, for example, JMock.
Integration tests are important too but the major drawback of them is that they take a long time to run. You can run thousands of true unit tests in a couple of seconds, but it's not the same with integration tests.
Depending on the size of your project/development team you might want to prioritize true unit tests over integration tests. Both style of tests are important but if you are pressed for resources, just going with Unit testing may be a better idea.
I wrote an application by myself that unit tested the Web (with Spring MVC this is easy) and Service layers, as well as domain objects. But I left the DAO alone because I didn't want to write a bunch of slow integration tests. If I had more people on staff I would have gone with integration tests as well, but in this case I didn't feel the time spent would be worth it.