Why do all the planets of the solar system orbit in roughly the same 2D plane? 
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*Most images you see of the solar system are 2D and all planets orbit in the same plane. In a 3D view, are really all planets orbiting in similar planes? Is there a reason for this? I'd expect that the orbits distributed all around the sun, in 3D.

*Has an object made by man (a probe) ever left the Solar System?
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*More or less yes.  The planets mostly orbit in the same plane but with small deviations compared to the size of the system.  The largest relative tilt is around 4 to 6 degrees. This 'flatness' is due to orbital mechanics, where the solar system started spherical it now has 'decayed' into a flat disc.  This disc is essentially a stable low energy configuration and therefore the system has become more and more disc like over time.

*The Voyager 1 probe is 'leaving' the solarsystem as we speak but there is no real firm boundary and so it's hard to give a definitive answer.
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*The orbital planes of different planets has small inclinations to the ecliptic plane. The corresponding wikipedia diagram should give a better view than the 2D images you've seen.

*Both Voyager 1 and 2 are beyond the Solar System
A: Nic and Approximist's answers hit the main points, but it's worth adding an additional word on the reason the orbits lie roughly in the same plane: Conservation of angular momentum.
The Solar System began as a large cloud of stuff, many times larger than its current size. It had some very slight initial angular momentum -- that is, it was, on average, rotating about a certain axis. (Why? Maybe just randomly! All of the constituents were flying around, and if you add up those random motions, there'll generically be some nonzero angular momentum.) Because angular momentum is conserved, as the cloud collapsed the rotation rate sped up (the usual example being the figure skater who pulls in her arms as she spins, and speeds up accordingly). 
Further collapse in the direction perpendicular to the plane of rotation doesn't change the angular momentum, but collapse in the other directions would change it. So the collapse turns the initial cloud, whatever its shape, into a pancake. The planets formed out of that pancake.
By the way, you can see the signs of that initial angular momentum in other things too: not only are all of the planets orbiting in roughly the same plane, but so are most of their moons, and most of the planets' rotations about their axes as well.
A: We don't know, but there what I gather is the typical pattern of hypothesis, accretion disc theory, which attempts to find a model dynamic that could explain what we see, particularly in our own solar system, which is the only one we have very complete information about. In addition to seeing that our own solar system's planets all orbit in the same plane, we can also observe many disc distributions around other strong gravity wells, which we also call accretion discs.
As I understand it, the reason for most orbiting matter to end up in the same plane goes something like this:
I think the assumption is that there was a lot of dust fairly homogenously distributed over a region greater than the solar system. Conglomerations convert the dust into a random distribution of globs and gravity eventually pulls most of the globs into larger globs (protoplanets) which have growing escape velocities while enough dust remains. The globs combine until most of the mass is in one large concentration or another, typicaly one largest one, but sometimes two or more.
Just as gravity pulls most nearby dust at a similar velocity into the largest local accumultation, joining it, a system full of globs (orbiting a protostar in a random spherical cloud of orbits) would have the globs interacting with each other by gravity, resulting in unstable paths and more and more collisions. The more an orbit gets randomly changed, the more likelihood of it hitting something (proto-star or proto-planet globs) and joining it, and also cancelling some velocity in the collision. Even though inertia would still fall towards a random cloud of orbits in no particular plane, once the cloud randomly ends up with any amount of concentration of large globs in the same rough plane, that plane will have more net attraction, and more chances for collision capture, than other planes, and as that plane captures matter from orbits in other planes, the deviation will get absorbed in collisions, and the matter in that plane itself will be pulling on the other matter in that plane, resulting in more and more deviation-cancelling collisions in that plane. I.e. It would be a positive feedback loop effect. However, the stages and numbers involved though are all unknown, so even if the theory makes sense, the actual situation might not tend to work out that way, because the theoretical effect might not be anywhere near enough in practice to have the result we see. We don't know both because we don't know the details of the initial state that formed our star or others, and I think it would be a daunting task to try to model the progress of any such over so much time (and to do it many times to see trends and possibilities).
There is also an effect where energy taken from the rotational momentum of matter being pulled into a mass is released in bipolar jets, which I don't quite get the physics of, but others do, and there are spectacular observations clearly showing it.
A possibility that occurs to me, is that maybe what actually happened, either just in our case, or maybe in most or all star formation, is that two enormous dust fields with different overall velocities intersected - that intersection (it seems to me) would tend to be a plane locally, and would result in friction, velocities and concentrations focused in one plane from the start. Maybe dust clouds stay dust clouds except where two dust clouds with different velocities and sufficient density meet in the right way, and this tends to lead to an orbital plane, along with the tendencies in the accretion disc theory.
However, having said all that and looking through various articles to check it, I ran into a pretty great site full of explanations of things with an Accretion Discs section that goes into lots of detail, which I highly recommend: http://www.scholarpedia.org/article/Accretion_discs
