You can develop good personal relationships with a judge or judges.
You may be able to deal with several different types of law. I dealt with a lot of criminal, but I also wrote orders for several different civil case.
You learn to tailor large amounts of research into an acceptable document.
You learn how to streamline the writing and research process because you will usually use templates written by previous clerks and judges.
The hours are usually pretty great.
Prospective employers seem to think the experience is valuable enough, at least for a first summer job.
You will have the opportunity to watch a lot of proceedings in court. I watched a few murder trials from start to finish, a few custody proceedings, countless preliminary hearings, and a couple civil trials.
Your judge could possibly only deal with one field of law, and you might not like it that much. A firm position might allow you to get a wider range of experience.
you could get pigeon holed as an "aspiring litigator." Some employers I interviewed with looked at my clerkship experience as evidence that I was going down the litigation track.
You probably won't get paid (but you can probably get law school credit, even though you have to pay for it)
Clerkships usually require an early commitment, so you might miss out on some other opportunities that pop up.