There's no clear yes/ no answer to this question.

I enjoy sharing this video everytime this question pops up! just to prove it's not a "cultural thing".

https://www.youtube.com/watch?v=T_lh5fR4DMA

You know, in Russia some people say, that even friendship between two women doesn't exist, because one is supposed to envy and gossip about the other...

Some people, I heard, believe, that true love doesn't exist, because they can't find it...

Some say that God doesn't exist, because they can't see him...

As for me, friendship between a man and a woman could exist.  :)

The video Mumtaz shared is interesting, but I do not think it proves the point that men and women can not be friends.  One thing I noticed in the video was that they talked about ¨hooking up¨.  I do not know if all English learners are aware of the connotations of this phrase. If you don´t here is a link of several definitions¨: http://www.urbandictionary.com/define.php?term=hooking%20up  

Heterosexual men and women who are friends are likely to have some sexual attraction to each other, but can often choose to keep the relationship in the ¨friend zone¨ quite successfully, especially if one (usually the woman) chooses not to express the sexual attraction to the other or to flirt in any way with the other.    In the video the respondents were young people at a university. Given the typical high sex drive of men at this age,  It did not surprise me in the least that the men admitted that if they knew the woman wanted to hook up with them they would be happy to do so. Chances are many times that would convert the relationship into ¨friends with benefits¨, not into boyfriend/girlfriend.  

I still think it is very possible for men and woman to just be friends, even when there is some sexual attraction. A good friend will not try to coerce another friend into a sexual relationship when there are not clear signals that that is what is wanted. Many men and women are capable of this, especially when one of the members of the friendship is in another romantic relationship.  It is posslble to love more than one person but never convert a relationship into a sexual one.  

If one of them is gay, yes that could be possible.

Otherwise, I don't believe it.