Is it true that women go for men that do not like them?

No not nessesarally, but as social animals we do have a tendency to want to be liked, which can lead to this assumption sometimes.

Or is it a matter of the men playing hard to get making it more interesting?

The age old adage is that people always strive most for that thing they cant have and a common tactic by both sides to maintain intrest is to fain a lack of interest one's self...to an extent.

Do we not value what we have?

A lot of people seem to take what they have for granted until they no longer have it. Absence makes the heart grow fonder.

Is it more fun if others want it too?

Sometimes it can be.

Or do we really like the ones who like us?

I don't believe an "eaither / or " statement to be aplicable in this case.

Are men any different?

According to the science of medicine they are different not only in their gross anatomy, but on the cellular metabolic level as well. It is no wonder then that their brain chemistry and hence phycological disposition and the inhierent behavioral responces that come with it, is also not quite the same as that of the fairer sex.