Shooting run and gun style can be very challenging, even with the "smaller" DSLRs that many people use these days. I have found a combination that I've come to use almost every time I can't have the camera on a tripod.
It consists of:
Canon 5D Mark II - Pretty self explanatory.
Canon 24-70L Zoom Lens - Good zoom range for nearly everything you'd run in to and the f/2.8 is pretty decent for low light.
Small HD DP4 w/ Lens Hood - This is essential with its focus peaking feature. I use the hood as opposed to the viewfinder attachment when I'm running around because its lighter and I don't have to have the camera up to my face to see what I'm filming.
Monopod - I use a simply, light weight monopod just to stabilize the camera on. You can also use it as a sort of poor mans stedi-cam which can be helpful when you have to walk (or run) and film at the same time. Its also more comfortable when your waiting for shots or taking a breather to just rest the monopod on the ground, vs having to hold a shoulder rig all day long or finding somewhere to set it down without risking your gear.