(Oh, come ON. Like somebody wasn't going to use that title at some point this week, seriously.)
Critiquing is one of the most important things you'll do as a writer. I don't just mean finding yourself a crit partner and handling their work while they handle yours. Heh heh. Because although crit partners are important, and having another eye to check your work over is valuable, I'm not entirely certain it's better than actually doing critiques yourself.
See, you're too close to your own story. You know exactly what everyone is thinking and feeling, you know what they're going to do next. So when you read it yourself, your mind absorbs all that unwritten information along with what's actually there. This is why everyone who's just starting out thinks they are the greatest writer in the world.
You will never see the mistakes in your story and writing until you start seeing them elsewhere. This is why critting other people is so important.
You'll find a piece that doesn't read right, and you'll analyze it. Perhaps they have ten sentences in a row that follow this structure: "Verbing the noun, she verbed the noun." (Obviously there would be actual verbs and nouns in the story. This is the Mad Libs version of critting.) The sentence itself may be fine; "Opening the cabinet, she grabbed the peanut butter." It's not a great sentence. You should be able to think of several other ways to say it without doing that comma thing and implying that all action takes place simultaneously. But it's not awful as it stands, really, and can be useful in certain places, used very sparingly (and when the action in question really is simultaneous).
But picture it ten times in a row. "Opening the door, she took out the peanut butter. Grabbing the knife, she dipped it in the jar. Picking up the bread, she..."
You might not notice this in your own work. But you'll notice it in someone else's, and it will skitter up your spine like a ball of tinfoil and set your teeth on edge, and so you will learn to look for it in your own.
There are a lot of things nobody teaches you about writing. Even books like Self-Editing for Fiction Writers, which is one of the few books I've found really valuable, don't tell you everything. Like how to structure a story. How to hold information back and let it spill out in drips and drabs. What sorts of similes and metaphors work and which don't, which are cliche. How bad it is when sentence structure is off or when too many pronouns are used so you don't know who's doing what to whom and where.
A lot of this you should know simply because you read a lot of books (don't you? Because if you don't you have no business trying to write some of your own, sorry to say.) But if you read good books, you don't get a chance to see bad ones. I personally learn a lot more--or at least did in the beginning--from bad prose.
Not to mention the most valuable lesson, I think, which is being able to read a piece and know that, while it may be very good, something is missing. The dialogue doesn't sparkle, or the voice isn't compelling. This is the biggest bugaboo, the thing that keeps technically good writers from leaving the slush pile. In time you'll be able to recognize it, and see how you can avoid it in your own writing. You'll realize when someone is being too safe, or when they could cut out sections of dialogue and make conversations shorter and snappier. You'll see how if they'd just punched up their opening you would have been enraptured enough to forgive that paragraph of necessary exposition on page two, but as it is they're just not grabbing you.
And you'll learn another valuable lesson, which Anton mentoned yesterday: that critters really are trying to help, that they're not trying to be mean, and that when you put in the time and effort to try and help someone improve and they turn around and slap you for it, it feels lousy. So in giving criticism you learn how to take it, which is pretty hard to do.
And I'm sorry this post isn't the greatest. My six-year-old is home sick and refuses to stop yelling and singing no matter what I do, and I can tune out a LOT but not endless tuneless repititions of "Twinkle Twinkle Little Star" sung at the top of six-year-old lungs.