Is it feasible for an unmanned vehicle to travel from outside the atmosphere of one planet to another without additional propulsion? Within the Solar System (or any other system for that matter) - 
Is it feasible for an unmanned vehicle to travel from outside the atmosphere of one planet to another without additional propulsion? That is to say
Given a vehicle in orbit around a planet, say Mercury, suppose a body were launched with the destination Earth with the caveat that it have sufficient velocity to travel the distance so it reaches Earth at velocity necessary to be at Geosynchronous orbit. 
Could this be achieved merely by using launch velocity so that the launched body does not need carry it's own propulsion?
 A: In a word, yes. The concept of the mass driver has this kind of launch in mind. All you need to do is accelerate the vehicle to the escape velocity at the point of launch (in fact, you don't even need to do that - you can simply put the vehicle into a sufficiently elliptical orbit that intersects with the target planet at apoapsis - for infinitely distant targets the velocity required to attain this orbit converges to the escape velocity). What you do when you reach the target planet (get gravitationally captured, crash lithobrake, adjust orbit with thrust, etc) is up to you.
Bear in mind that most space probes would spend almost all of their time in freefall (that is, not under thrust). Ion thrusters are an important exception as far as I know.
A: Without a third body to interact with at the arrival point, then "no", it is not possible to take up orbit when you get there unless you have some thrust (but I'll say a little more about the weasel words in a minute).
The basic problem is that you arrive (by definition from far away) on a hyperbolic orbit and you will, therefore leave on a hyperbolic orbit.
Exceptions:


*

*You hit the target (that's Richard's "lithobraking") or at least it's atmosphere (areobraking) and lose a lot of energy that way.

*You are going "uphill" and can lose the hyperbolic energy to the Sun's gravity. (I've not actually seen a complete calculation for this, but I think that the mean value theorem requires it to be possible).

*There is a third (or more) body nearby and you can trade some energy with it (them). Again, I haven't seen any calculation and they will be tedious and exacting.

*You have some kind of thrust that is discounted by the question. Perhaps a solar sail.

