Great post by genre writer JA Konrath on his blog today on How NOT to start a story.
My favorite is starting with weather. Yeah, don't do that, for crying out loud.
I'd add - Don't start (or ever write) with a scene where your character is looking in the mirror, describes themselves physically, or speaks to themselves.
Don't start with a dream.
You'd be shocked how many writers violate these basic rules. Sometimes they do get published. Sometimes the books are actually good and succeed in spite of beginning with a mistake. Konrath says not to begin with a description of character, but I vividly remember the first sentence of Gone With the Wind: "Scarlett O'Hara was not beautiful..." which goes on to describe how fascinating she is with her green eyes and inky lashes. GWTW is a terrific book and (I think) the top selling novel of all time. But notice that even if Margaret Mitchell starts with a character description, she goes against expectations by telling us the main character is NOT beautiful.
How do you start? There's no one answer, but I recommend starting with your protagonist in action. That doesn't mean he or she has to be gunning down bad guys in the first sentence. They could be picking up their handicapped kid from therapy or confronting their girlfriend about her cheating, fleeing an abusive husband, or... gunning down baddies. Action shows us who that person is in an entertaining way. Action will force you to show us who this person is, rather than tell.
UPDATE: I apologize to JA Konrath, whom I referred to mistakenly as "her" when I wrote this post. Konrath is in fact a man, so I've edited this post to reflect that.