I often have summer interns, but it's hard to predict in advance. If I do have summer internship openings, I will use this page to advertise them. When I do have summer internships, it's usually to address some research goal, and the internships are paid. Regardless of that year's research topic, the minimum requirements are basically the same:

• Fluency in C - most of my group's research is done in C, and we tend to maintain our software for a long time. So, for practical reasons, we've stuck to C for basically everything we do. If you're not really comfortable with C, it's not going to be a productive summer.
• Legal right to work in the US - due to the short lead times and the large amount of paperwork involved, Princeton typically does not sponsor visas for summer internships. For people applying to our graduate program, this is not an issue, since the system already has lead times, etc., built into it. However, for summer internships, I really need someone who already has the right to work in the US since we can't sponsor a visa.
• Preferably, the equivalent of our Operating Systems or Networking courses - since my group's research is in systems, it helps to have this level of background. Most of our internships are research internships, not grunt-work internships. The idea is that it lets you experience a research environment, and to see if you would like graduate school later. Very rarely do I hire someone to "just do some programming". It happens, if I need something done, but it's rare.

So, with all of that said, here's what we don't do: unpaid internships and job shadowing. I think unpaid internships are not a good idea for promoting a healthy discipline, and it's biased toward those who can afford it. I don't see the point of unpaid internships. Likewise, job shadowing me amounts to watching me respond to e-mail, have meetings, drink coffee, and program. I don't see what it gains, and I wouldn't feel comfortable having most of my meetings with someone shadowing them.

Current status: no internship openings at the moment