I know of the following airlines that have interns in the flight operations department:

• Northwest
• Delta
• American
• jetBlue
• Southwest
• Continental / CoEx
• ACA
• Evergreen

There are probably more and they afford the interns excellent opportunities. Work in the chief pilot's office, the flight safety department (ASAP or FOQA or other), take a groundschool course, take indoc., fly the sims, jumpseat on the line, and in general get to see how an airline works and work with some high-up people within the company on a daily basis.

As far as I know, all of them are gotten as an undergraduate and that is listed as a requirement.