I've got a pretty big problem with this, too. I have always assumed it'* due to cheap brake rotors that warp easily, but I'm not completely sure. Icebound was correct to suggest tires and wheels, because a tire with a broken belt or bulge can easily throw the ride out of balance. With wheels, if a wheel weight gets thrown you can feel significant vibrations, though I don't know if it would be any worse braking than accelerating.
We'll wait for a more experienced member to step in and give a little guidance
. In the meantime, you might want to consider how long it has been since your pads and rotors were last changed, and whether your tires are close to the point of needing replacement.