Appropriately enough, I'm thinking about beginnings this morning. What I've got to introduce myself I've put in the About me page, so let's talk about story beginnings instead.
I like to start where everything changes. Sometimes it's a big change, like a death; sometimes it's a small change, like a promise, but it's still a change. Whether this change happens in the first sentence or later depends on the length of the story: in a novel that change had better at least be hinted at within the first ten pages or the reader will get bored.