SR4 Insurance Fraud is an amazing abuse of the physics engine. You could combo forever using your Matrix powers! There's no target area, so once you're high in the air or cartwheeling on the ground, you can flip into cars, fly into the air, dive into a car, and repeat ad infinitum. I've gotten gold medals from a single combo this way. Much easier than SR3.
The "destroy $X worth of stuff" missions are the ones I struggle with. It's hard maintaining a combo.
My favourite activity is... oddly... collecting the data clusters. If I see one, I will go for it.
The destruction of the Physics engine is pure bliss