Does water have surface tension in a vacuum? I could be totally wrong here but I was thinking about water surface and what creates that. My thought is it is the thin mixture of water and air separating the two. This mixture creates the boundary between water and air that has the property of surface tension. 
So does the surface of water in a vacuum act in the same way? Is there a surface with surface tension when there is no air to make the mixture?
 A: Coming to the party late... but consider this:
The surface tension of the liquid is a result of the intermolecular forces of the molecules in the liquid . The fact that there may or not be molecules in the space above the liquid does not change the presence of these forces.
When we talk of a liquid "boiling off" at very low pressures, we are really saying that the equilibrium state of the liquid with a vapor is such that at sufficiently low vapor pressures, the liquid cannot exist (see the phase diagram in Superbest's answer). 
Another way of looking at that: at "normal" pressures, there is a highly dynamic equilibrium between molecules in the liquid (some of the more energetic of which will escape into the vapor, taking some energy with them) and molecules in the vapor (some of which will "slam into" the liquid and stay there, depositing some energy in the process). At a certain temperature, the corresponding vapor pressure is such that the two processes happen at the same rate.
When you remove the vapor molecules (with your "perfect vacuum"), you upset this equilibrium. Thus, molecules escape the liquid, but they do not get replaced. The liquid will get progressively colder, and its volume will decrease. Then one of two things happens: either it gets cold enough that it solidifies (and now the force holding the molecules together is much greater - although there will be some sublimation) or it evaporates completely before it has a chance to solidify (depending on the initial temperature).
Nothing in the above fundamentally changes the fact that there are intermolecular forces on the liquid while it exists; these forces are a weak function of temperature, but they do not depend on the existence of an atmosphere above the liquid.  Thus I think the answer is:
Yes a liquid in a vacuum will have a surface tension; but the liquid will not be able to exist in the vacuum forever.
How rapidly it will disappear will in some sense depend on this surface tension (the intermolecular force) since the energy needed for a molecule to escape the liquid is closely related to this intermolecular force.
A: Yes, water still has surface tension in a vacuum.  
Water/vacuum surface tension is 72.8 dyn/cm experimentally according to Zhang et al. J. Chem. Phys. 103, 10252 (1995).
Surface tension is caused by the fact that water molecules in the bulk (not at the surface), are surrounded by other water molecules with which they interact through intermolecular forces.  At the surface, the molecules cannot be completely surrounded by other water molecules.  The surface molecules are in a higher energy state because they are not stablized by intermolecular interactions. This is why liquids tend to miniumize surface area and become spherical droplets absence any other forces.   
Also, the attractive force from other water molecules on the surface molecules has a net force in the direction toward the interior.   
