To what extent do individuals vary in their ability to mentally visualise? Background:
Yesterday I was shocked when a friend of mine told me that he can see only "completely black darkness" when he closes he eyes.
When I close my eyes, I can see some images or "movies" of what I'm thinking of just now. I don't see the real world. I can "imagine" anything I would like, e.g., a car crash or a sunshine or someone who I know or who I do not.  I also can control them in any way: change colors, action, everything. I was sure that anybody on Earth can do it.
Indeed, when I asked him if he could "see" even a simple figure, e.g., a circle - he couldn't. He said he could not see anything.

Questions:


What is this "phenomenon" called where a person cannot mentally visualise images when they close their eyes? 
Are there many people who can't see anything with closed eyes?
Short answer: there appears to be a whole range of ability at the task of mental visualization. Based on what I have found on the Web, your own level of ability is fairly unusual. Your friend's level of ability, by contrast, seems to be fairly common. Sources I found on this were fairly sparse, though, and my conclusions should not be relied on too heavily.

The Wikipedia article on "Closed-eye hallucination" seems to have some problems, but is helpful on this question. It describes five distinct levels of "Closed-eye visualization."


Levels 1 and 2 correspond to very little visual information.
Level 3 is "patterns, motion, and color."
Level 4, "objects and things," appears to correspond to your experience.
Level 5 describes impressions not immediately distinguishable from reality.



  Level 1 and 2 are very common, and often happen every day. It is still
  normal to experience level 3, and even level 4, but only a small
  percentage of the population do this without psychedelic drugs,
  meditation or extensive visualization training.


Wikipedia also links an old paper in Psychological Review that studied variations in the ability to willfully shape closed-eye perception, describing what seems to be a wide distribution of ability:


  Of the sixteen persons experimenting with themselves, four only
  reported no success; nine had a partial success which seemed to
  increase with practice and which they considered undoubtedly dependent
  directly upon volition; and with the remaining three the success was
  marked and really phenomenal.


I seem to remember that there was an early debate in psychology about whether it was possible to mentally visualize images. Some scholars insisted that it was, others were adamant that it wasn't. Today we can dissolve the debate because we know it is possible for some but not for others. Unfortunately, I can't find a source for this story online.

There is also an old debate in philosophy over the role mental imagery plays in cognition. For some early thinkers, an "idea" was a visual mental image; other philosophers questioned whether actual images were so important. For an overview of the debate you can consult the topic "Mental Imagery" in Stanford's Encyclopedia of Philosophy. The mental imagery debate is not really the same thing as what you're asking about, but participants sometimes seemed to be debating whether it was even possible to "see" mental images.