You can't slow down at constant speed, so I assume you mean constant acceleration (acceleration is the rate of change of velocity and can be used to describe slowing down, speeding up, or even turning at constant speed (since velocity is a vector quantity))

Are you talking about hitting the brakes hard so the wheels stop rotating, or gradually pushing them down to ease to a stop like you're supposed to?

I don't have firsthand experience because I don't drive a car, and when I ride in one I'm not really paying attention. But as you are slowing down, yourself and the car's body lurches forward due to inertia, putting strain on the car's suspension, compressing the front shocks and stretching the back shocks. So I guess those springs snapping back into equilibrium when the car finally stops can cause a jerk.

If you keep your foot on the brake pedal and hold it in one position, then you apply a given force to the rotors via the brake pads (which are usually composed of an aesbestos or ceramic material with a high friction coefficient). As they apply that "frictional" force to the rotors by squeezing together, then the rotational energy in the rotors (attached to the hub and then the wheels) begins turn into heat, etc...you slow down. Now, at some point the force that is turning the wheels (torque) is going to be reduced by the frictional force of the brake pads sufficiently enough that it can't overcome the frictional force of the brakes and you lock the rotors, which locks the wheels, which causes you to come to an abrupt and lurching halt as teh remaining forward energy is transferred to the chassis and suspension (as Lead stated).

As most everyone learns, you can prevent this by taking your foot off the brake slightly as you come to a stop. Basically you are reducing the brake pad force on the rotor so that the quickly diminishing torque is never overcome by the brakes until the energy in the system is so minute that when friction finally does win out...you are basically stopped anyway.
"Most" 16 year old learn this trick after thier dad yells at them sufficiently.

I usually just attribute this to the flux capacitor in my DeLorean. Could be what Giller said though...If only I had a DeLorean. Although I figured that it would be hard to get out of that car in even a medium-tight parking spot.

Giller - even if you're just lightly on the break, there's still that little pop of forward movement. I guess no one read my spoiler tags since all you guys did was say "you were right, Muff" without any humor. =\

A little Pop of movement? if you break right this shouldn't happen and is probably the result of you having something wrong with the vehicle. Could be a completely shot rotor and the pad is grabbing, or something wrong with front end that is popping loose when enough force is present. Could be a bushing somewhere or a ball joint. You should get it looked at. That, or you are a bad driver....

My car doesn't halt movement abruptly unless i want it to. even at less than 1 mph.

You call a DeLorean comment "without any humor"? I thought it was funny/clever.