This question is for Airborne graduates. Are there any good workout routines that you used to increase fitness prior to school?

Run and pull-ups.

Run up hills, preferably winding ones (Snake Hill stinks, if memory serves) and like everyone else has said, practice doing pull-ups from the hanging start, ensure you do proper push-ups (the Jumpmasters will look for ANY reason to boot people out, especially Officers) and get used to accordion running, at least until Tower Week.

Practice slinky run!