I tend to favor cycling myself, but being as I live in a busy area I normally don't do it purely for health reasons. I like jogging but that can be a bit rough on the knees unless you're running through soft terrain (like grass). I'm of the same opinion with jumping jacks, though they really know how to work on my calves and get my pulse going. I've heard swimming is the best when it comes to exercise in general.
Have you tried pilates? I haven't done any since high school but from what I know about them is that they're low stress, so you're less likely to strain anything doing them. They're something I'm considering since they have tapes at the library I can borrow.