Why is space a vacuum? Why is space a vacuum ? Why is space free from air molecules ? 
I heard that even space has a small but finite number of molecules. If so, won't there be a drag in space?
 A: Space is sometimes described as a vacuum better than mankind could create in any laboratory. But it is not a vacuum, but a tenuous plasma carrying the interplanetary medium (solar wind). It is also structured, forming the Heliospheric current sheet.
This means that space has the characteristics of a plasma. It is electrically conductive, carries magnetic fields, and carries energy from the sun resulting from coronal mass ejections that interact with the Earth's magnetic fields to produce the aurora, and can sometimes knock out the power to cities (eg. The Quebec Blackout)
The Solar Wind drags the Earth's magnetosphere out into space forming its magnetotail. It is the same principle as a "magnetic sail". The drag is small, but significant if you are an ion in space.
A: First, space is not a complete vacuum. You still have some particles going around in there.
In common mind, space is empty, but it is only "empty" because you have some massive particles in it (like planets, stars etc.). Around these particles you have a strong gravity field (of course in the other, "empty" regions you have that too, but only very weak compared to the near field around the planets). In this near field you have a much bigger accumulation of molecules than in the far field simply because of gravity. The less gravity (and the less escape speed) the less molecules you have around a planet or a star. Without additional masses in space (i.e. if all molecules are distributed equally) you would have a lot more molecules at several points (where we don't have some or fewer than now), but at some other places you have a lot fewer molecules (let's say at the place where earth was supposed to be.
So, if molecules are fast enough for escaping the near gravity field of a planet, then they are travelling around in space. If they are too slow, they form an atmosphere around a planet which is an explanation why we have atmospheres around several planets, but not around all (moon, for example). 
A: 
Why is space a vacuum ?

Because, given enough time, gravity tends to make matter clump together. Events like supernovae that spread it out again are relatively rare. Also space is big. Maybe someone could calculate the density if visible matter were evenly distributed in visible space. I imagine it would be pretty thin.
(Later)

Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space.

Douglas Adams, Hitchiker's guide to the galaxy.
According to Wikipedia, the observable universe has a radius of 46.6 billion light years and contains about $10^{53}$ kg of matter.
One light year is about $9.5 \times 10^{15} m$  - so that is a radius of roughly $4.4 \times 10^{24} m$ and a volume of roughly $2.73 \times 10^{80} m^3$ So that means a density of $0.366 \times 10^{-27} kg/m^3$ 
If that matter were all Hydrogen, which has $6 \times 10^{26}$ atoms per kg, that would give us around $0.2$ atoms per $m^3$.
So if my horrible calculations are any guide (and I'm very likely to have made an error), space is a vacuum mostly because the amount of matter in the observable universe is negligible.

Why is space free from air molecules ?

Well, air is what we call the mix of gases in Earth's atmosphere, so this is a question about space near Earth specifically.
Air is mostly molecular Nitrogen and Oxygen - $N_2$ and $O_2$. These are heavy enough that not many of them escape Earth's gravity. Also, space is big.

I heard that even space has a small but finite number of molecules. If so, Wont there be a drag in space?

According to WIkipedia:

Intergalactic space contains a few hydrogen atoms per cubic meter. By comparison, the air we breathe contains about $10^{25}$ molecules per cubic meter.

That is such a large difference that space is effectively frictionless (at least for typical space vehicles constructed by humans).
Bumping against 1 hydrogen atom is very different to bumping against 10000000000000000000000000 Nitrogen molecules.
A: Sorry for being oxymoronic here, but your questions (OP) are in their very meaning, illogical. I mean to say that you have used extremely misleading terminology to present your question. I am unable to understand what exactly you intend to ask.

Why is space a vacuum?

Space is a vacuum because the word vacuum means "empty space". If the universe had no emptiness (almost emptiness, as the posters before me have stated), we would not use the word "space" for it. So space, by its very definition in English language, is emptiness. Its like you are asking "why is blue color kinda bluish?"

Why is space free from air molecules?

Same as above. Because by definition, space = emptiness. In emptiness you do not have any air molecules, but just plain void. However if you intend to ask (assuming in good faith) that why the vast distances between heavenly bodies have almost negligible matter, then the answer (just simplifying the posters above me) is that if matter was evenly distributed in the universe, gravity would serve to gradually accumulate it into heavy, dense objects (that's what gravity always does, provided you don't counterbalance it). Plus here I must say that if all the matter in our universe was not moving at incredibly fast speed, gravity would gradually clump up ALL the matter into a single unbelievably horrific black hole (an object with huuuuuuge mass and veryyyyy tiny volume, like compressing an ocean into a glass of water). Universe has matter spread out and in the form of different objects (stars, galaxies, planets, moons, gas/dust clouds etc) is because all the matter in our universe is running very very fast away from each other, which enables it to escape from being clumped together into a horrific black hole.

I heard that even space has a small but finite number of molecules. If so, won't there be a drag in space?

You are right here. Yes, there is very very very small amount of matter spread out in the emptiness between stars, but thats just too less to make a difference for large objects moving there. You are right, there IS drag in space, but that is just incredibly less to have any influence at all. Will a paper wall, 0.001 mm thick, placed in the path of a train of mass 2000 tons, make any difference on the motion of the train? Yes it will. But it will be ALMOST zero. The resistance offered by freely roaming molecules in space offer an even lesser drag than that paper wall.
