Many, many references exist detailing that Dustin Hoffman's character was based in large part on Kim Peek, an autistic savant who exhibited a lot of the characteristics that Hoffman portrays. I think the key here is that there's a difference between being autistic and being a savant -- those are two distinct syndromes, and they don't often go together. Some of the things in your list would be a symptom of being a savant (eidetic memory, counting skills, etc), while others would come from from autism (and many of the things you list -- obsessive/compulsive nature, fears, minimal interest in people, etc. are known symptoms of autism in varying degrees). So what you see in Rain Man does happen, but is quite rare.
As a side note ... when I was 12, Kim Peek came to speak to our Junior High, and he really was like you see in the movie -- you could give him a date in history and he'd tell you what day of the week it happened on (adjusting for leap years, changing calendars, etc.), and he memorized the order of 3 shuffled decks of cards in a matter of seconds.