Think about the momentum in the two situations. In any closed system, momentum must be conserved. When you accelerate a car, you push the Earth in the opposite direction with exactly the same momentum. When you want to slow down (which again is acceleration, just in direction opposite to motion), you again push the Earth, and it will be accelerated in the opposite direction. Since the Earth is much more massive than the car, the acceleration on the Earth is tiny, which makes Earth easy to push from (compare jumping on concrete with jumping on a bit of foam - the concrete is almost unyielding, which gives you a lot of leverage).
The braking and acceleration are symmetric in this case - when accelerating, you make the car move faster relative to the ground, when braking, you make it slower relative to the ground. Slowing a fast thing down on a slow thing allows you to extract useful work, pretty much the same way you can extract work from, say, an interface between a high temperature and low temperature object, or high pressure and a low pressure system.
But that's not the case with a spaceship in free space (i.e. where we can safely ignore gravity, space dust etc.). There's no simple way to "push off" anything in space - so you carry your own "pushing mass". Momentum is still conserved - if you look from a frame of reference where the original spaceship is motionless, accelerating will make you see the spaceship moving in one direction with a given momentum, and the propellant (the mass you throw backwards) will have exactly the opposite momentum. Together, the total momentum is still zero - but relative to the fixed point, both masses have been accelerated, and both have their own momentum. That's how we can get to other planets, despite having no roads to push off - that's the difference between a jet airplane (which uses ambient air as propellant) and a rocket (which needs to carry both fuel and propellant).
Now imagine what would have to happen if you were to brake similar to a car. You'd somehow need to get the already expelled propellant back - imagine something like having two balls connected by a string. When the string snaps taut, the balls will "recoil", their direction of motion reversed, and they will collide at some point; if you are careful enough, you can accelerate one ball by throwing the other ball in the opposite direction, and when the string runs out, they will stop again. The problem is, just like the momentum is conserved, so is the center of mass - somewhere between the two balls, the center of mass is at exactly the same position as before the acceleration and subsequent deceleration (or rather, it's where it would have been if you didn't accelerate in the first place, as long as we can assume interference with e.g. the atmosphere or gravitational field etc.). The only reason rockets can move in space is that the propellant is not connected to the rocket anymore.
If you could have a magical string that allowed you to connect your rocket to its propellant and draw it back, you could brake the rocket "for free". But you'd also pull the rocket back to where it started. Now, mind you, in a planetary system, this could still be used for transportation, and it would be a revolution in spaceflight - you'd use gravitational maneuvers with your target planet to steal some of its momentum, which would allow you to draw the propellant back with more "leverage". But we have no such magical string, and no other way to move in free space.
We do have a few tricks, though. Aerobraking and gravitational assists are both ways of exchanging momentum with planets (and other massive bodies), and as such, they are very different from the rocket engine itself. Momentum is again still conserved - each such "push" changes the motion characteristics of the body in question; it might slow down its orbit, or make it faster, or slow down its rotation or make it faster. But since we're again dealing with objects much more massive than your spaceship, we're back to "essentially free". And indeed, we use these maneuvers extensively - our capabilities are so limited that we can scarcely afford not to. Remember those brutal reëntry videos of the space shuttle and similar craft? Huge speeds, huge temperatures, huge stress on the spacecraft? They are only necessary because we don't have spaceship engines efficient enough. If we had rocket engines that would use half the propellant/fuel mass for the same amount of momentum produced, spaceflight would get much easier, and we could easily avoid the dangerous reëntry with existing spacecraft (though it might be that we would simply build smaller spaceships to do the same thing).
Okay, so if we have something to push off, we can recuperate energy. Indeed, we can even recoup more energy than we originally used, if we just use the right trajectories between the right kind of massive bodies! But there's little you can reasonably do with that energy. We do have spaceship propulsion systems that run on electricity (they still need some propellant, they just need far less mass for the same amount of velocity change); but those are powered either by solar cells or RTGs - they have no benefit from recuperating the energy, even if it were practically possible. With our technology, energy isn't the biggest problem - propellant is. As long as we keep throwing mass out the backside of a rocket to produce a change in velocity, we'd need some way to get that mass back. The kinetic energy of the spacecraft is tiny compared to the mass-energy of the propellant. And the fun is, the less massive the propellant, the higher the efficiency, but the more energy input you need for the same momentum (momentum increases linearly with velocity, while kinetic energy increases with a square of velocity), and the lower the thrust. Most of the energy cannot be recuperated, since it's in the propellant, not your spaceship - and the more efficient your engine, the more energy is in the propellant as opposed to the spaceship. So in the end, the systems which would have the most benefit from recuperating the energy also need far more of it.
The holy grail of spaceflight would be a magical device that allows you to push off any object you want with as much force as you want - this would make spaceflight almost as easy as driving a car. Want to accelerate? Push off the planet you're leaving. Slow down? Recuperate the energy as you push off the target planet. It would work just like the electric engine in your car! Sadly, we have little reason to believe we'll ever be able to make such a device; it's not technically impossible in theory, but we know of no mechanism that would be adequate. One could imagine some orbital infrastructure that would allow us to exchange the momentum of planets with spacecraft being flung out from one planet to another, but certainly not for independent spaceships zipping along willy-nilly around the system.
