Did you mean which jobs in general, or which judge-related jobs?
Jobs in general, obviously some government jobs but it depends on what area you're working in and what sort of material you'll be working with. For example, I was offered a job with U.S. Attorneys' offices, and they require fingerprinting, drug test, financial history, 10 year job history, etc. But working for the U.S. Senate committee doesn't require anything. Anything where you're handling marketable, private information will require at least some sort of background information. Did you have anything specific in mind?