It depends. As far as judges go, state courts usually accept 1Ls as judicial interns, as do the chambers of many US District judges. Federal Appeals judges, from what I can tell, don't take on many 1Ls as interns, although individual judges might (I know of at least one judge on the 1st Circuit who does). If applying to state courts, try to get an idea from career services or some other source how the application process works. You might have to apply to the chambers of every judge you're interested in working with on an individual basis, like the feds do it; other states have you mail one application to a central office, and then automatically distribute copies to judges who have mentioned they're looking for extra help.
In addition, there are plenty of government agencies (both state and federal, examples including the attorney general's office, the revenue commission, the insurance commission, various departments and administrative agencies, etc.) that will accept 1Ls as summer clerks or interns, though it probably helps to have some background or interest in the substantive areas of law they deal with. There are also a lot of public interest groups, legal clinics, and LSCs that hire, and they provide great practical experience and potentially broad exposure to many different areas of law. Also small and mid-sized firms hire, but typically they can't predict what their needs for the summer will be too far in advance, so the timeline for application is substantially later (like, January or even February for small employers). Also look at inhouse and general counsel's offices at various private and public (like universities) corporations.
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