RE: 870 jam
I'd try a different brand of shells. Also, make sure you're using shells that are no longer than the chamber of the shotgun. The length of the chamber is stamped on the barrel.
If another brand of shells that are definately the right length for the shotgun do the same thing, you may have a bad extractor. A gunsmith could tell you for sure. However, this is not my first impression given that it's happened with three different shotguns, so I'd suspect it's an ammo problem. Also, make sure your chamber is clean. A dirty chamber can cause extraction problems.
I've never had a problem with 870's. They have always been completely reliable in my experience.
Mike