I use Eclipse, Ant, Liferay 6.1, IDE 1.5. I've been told that after doing a service builder build this is necessary. Is it needed in any other case (or even in that one)?

You should do a clean whenever you delete a java file (or something from service.xml to cover the service builder). Possibly also if you refactor a java class to a new name, although I'm not sure off the top of my head if the IDE will rename the compiled class correctly (probably, but you should check to make sure).

The whole ant build process will only compile java to a .class file, but it will not delete a .class that has no java source file.

Follow-up question: So is clean necessary, but not compile, since deploy does that step?

In these cases, yes you'd have to manually invoke clean and deploy will handle the full build (compile, package, etc.).