The
reason traditionally given for "its" being exceptional among
possessives in its lack of an
apostrophe is that the
English language (God bless her and all who sail in her) used to follow simpler
rules.
1) "Its" means "belonging to it, and is the only way to form a possessive.
2) Apostrophes are used for
contraction only.
Thus the original formation of "the dog's claws" would have been "the dog its claws." The "it" in the middle gets dropped, leaving an apostrophe instead. Writing "it's claws" would be equivalent to "it its claws," and hence
erroneous.
Unfortunately, this explanation isn't true. It's pretty neat, though.