I can see how, if you have a regex that does a lot of bounded repetition, you might want to use the {n,m} form consistently for readability's sake.  For example:
/^
 abc{2,5}
 xyz{0,1}
 foo{3,12}
 bar{1,}
 $/x
But I can't recall ever seeing such a case in real life.  When I see {0,1}, {0,} or {1,} being used in a question, it's virtually always being done out of ignorance.  And in the process of answering such a question, we should also suggest that they use the ?, * or + instead.
And of course, {1} is pure clutter.  Some people seem to have a vague notion that it means "one and only one"--after all, it must mean something, right?  Why would such a pathologically terse language support a construct that takes up a whole three characters and does nothing at all?  Its only legitimate use that I know of is to isolate a backreference that's followed by a literal digit (e.g. \1{1}0), but there are other ways to do that.