"I should know who the main character is by the end of the first paragraph. I should know his or her gender, name, age, and have a vague idea of his or her personality. Double points if you can slip in a primary conflict, too."
Immediately your reader is in. Invested. Familiar. Certainly, conflict and plot drive a story forward--but what's conflict, what's plot, without someone to invest in? Without a hero to be conflicted?
Be honest about your style, genre, and story. Not everyone is going to like what you write, and that's just how the dice fall. I think one of the most emotionally costly mistakes a writer can make is trying to please everyone and anyone--because it's impossible, and you'll only end up banging your head against a table (and probably scoring a gnarly bruise) while trying.
Write the story you want to write, and never be ashamed of it. In your first pages, put your style front and center. It should convey to your reader (or an agent) exactly what she's getting herself into. What kind of book is she going to get should she keep reading? I try to capture the mood, storytelling style, and important thematic elements early on, so I keep the right readers.
(Someone once suggested telling a mini-story in the first few pages to parallel the story your manuscript is going to tell. I think it's cute and quirky, but would only work for certain narrative styles.)
Don't feel bad about losing a reader in your first pages, because it just means he wasn't into what you're selling. Not everyone likes everything.
Balance action, conflict, and backstory. The most important thing to remember is that your reader is a lot smarter than you're probably giving him credit for. "Okay, so I'm starting this manuscript right in the middle of an event or conflict. So how will my reader know what's going on if I don't tell him?"
BZZZT. Wrong outlook! When was the last time you watched a movie that "started at the beginning"? That laid everything out on the table (and wasn't "Lord of the Rings")? Think "Pulp Fiction." There's a perfect balance to be struck between tossing your reader into a strange new world, and giving your reader enough of the setting, character, and voice so they can float along. Because that's all we're really asking for: the reader to float, head just above the surface. We want her to keep turning the pages, wanting to know what happens next--but we don't want her drowned.
And remember: action does not equal conflict. It's appealing to open your story with A) hero waking up into some alternate universe with complete amnesia, B) the middle of a battle, or C) dying. (I have started stories with all of these.) I know--it's exciting. It's bound to get the reader hooked, right?
BZZZT. Sure, action is great if you're novelizing "Die Hard," but what's more compelling to a reader at the outset is conflict. What are the stakes? Why is there tension? What does the hero have to lose right at the outset, and what are the barriers in the way of her getting what she wants?
That's the stuff of first pages.