My friend Razib poses an interesting question at Talk Islam asking for people’s definitions of these four terms. Here are mine:

• racism – bias pr prejudice towards an ethnic group.
  
• anti-semitism – hatred towards Jews (or culturally affiliated persons therof)
  
• islamophobia – fear of muslims and islam
  
• sexism – indulgence in gender stereotypes

It should be noted that all four are different things and not directly analogous to each other (as I have emphasized using italics above). It’s possible to hate muslims, for example,
but that’s a derivative emotion from fear. Only Jews seem to actually be hated
without fear. sexism can lead to misogyny (hatred of women) but there’s
a continuum. and racism can be quite mild, but should still be called for
what it is. I think racism and sexism are the most analogous, but
racism takes on gradations in a continuum that sexism cannot because
the question of who is or who is not a member of race X or Y is not as
clear-cut as gender (a binary value).

There’s some vigorous follow-up discussion at TI here that’s also worth a look (as is Razib’s concluding comment). I think that clear definitions are a prerequisite for discussion on these volatile topics.