Where does the angular momentum of the solar system come from? We inhabit a system with significant angular momentum:
http://www.zipcon.net/~swhite/docs/astronomy/Angular_Momentum.html
If our solar system formed by gravity gathering its material together to form the sun, proto-planetary disc, and eventually the planets, which all orbit in the same direction...
Where did this angular momentum come from in the first place, since angular momentum is conserved?
It does not seem possible to me that the formation of the solar system under gravity could impart this angular momentum on it, if it is a closed system. If it formed from a 'cloud of space dust', then it must have been present in that dust cloud, but where did the dust cloud get it from?
 A: A collapsing gas cloud is an open system. It loses mass, energy and angular momentum as it collapses. Even if the net angular momentum of the cloud is zero, after the collapse the final planetary disk can have a significant net angular momentum, and the ejected material will have the opposite angular momentum. What can not happen, and that's where your intuition is correct, is that all the material in the original cloud collapses into the disk while rotating in the same direction.
A: Even if the original dust cloud only had a relatively small angular velocity (which it might have had for all sorts of reasons), the process of collapsing would have amplified it. That is, the collapse process preserves the angular momentum, but it translates to a much larger rotational speed in the newly-collapsed system. Think of what happens to a spinning ice skater when she pulls her arms in. 
Where did the original dust cloud get its angular momentum? Since this is a relatively small amount of angular momentum we are talking about, there are lots of places it could have come from. For example, if the original dust cloud was formed by the coalescence of two smaller dust clouds which happened to collide, the collision would have imparted angular momentum to the system unless the two original dust clouds collided perfectly head-on. 
