There are three big things that you need to know about organ donation. The first is the most serious: There Are Not Enough Organs For Everybody Who Needs One.
The second is this: Nobody Is Going To Kill You In Order To Harvest Your Organs.
And the third is this 'un: We Can Use More Than Just Organs.
Point Number One:
There simply aren't enough organs to go around. Kidneys, livers, hearts and lungs, you name it: there ain't enough. The problem is particularly acute in minority communities, as there are certain immunity factors that make successful transplantation more likely if you transplant, say, a kidney from an African-American or Asian-American into another African- or Asian-American. People die every day--thousands of them--because they've run out of time on a waiting list. You can donate even if your religion recommends that you stay in one piece for burial (Orthodox Judaism has an allowance for donation; I don't know about Jehovah's Witnesses), even if you're old, even if you're sick with certain things.
Point The Second:
When you (or somebody you love) dies of trauma or some "allowable" disease, the folks who keep your body alive and the folks who decide if you're a donor candidate are NOT the same people. Likewise, if you're wheeled into an ER after a motorcycle crash during which you weren't wearing a helmet, nobody's gonna look at you right off and say, "Hey, this is a potential organ donor; slow down on that intubation, okay?"
There are no doctors looking covetously at your liver. There are no nurses who're gonna slip you a little somethin'-somethin' to hurry you along. We're in the business of exhausting all possible resources until somebody says "stop", at which point we turn the possibility of donation over to some totally other different group that's not associated with us.
Point Numero Tres:
Even if you leave your organs in bad shape, we can still use your tendons (for people who need knee or hip surgery), bone (for trauma), skin (burns), intestines (yikes) and other bits, like corneas, to help other people. On the back of my driver's license is the notation: ALL USABLE ORGANS AND TISSUES. My family knows to compost the rest and plant a garden on top of it.
Please make arrangements to donate. Tell your family and friends. Fill out a "Live, Then Give" card--you can search online for local organ donation organizations that can hook you up.
And, if you're not in the mood to donate, or the thought of somebody using your leftovers totally squicks you out, try this: Faithful Reader Hallie has started a fundraising effort for the United Network For Organ Sharing. They're a great group--they work on national policy to make sure that organs are distributed in the most fair way possible, raise awareness, and get people set up with new bits when they need 'em.
Hallie's dad got a new heart through their good offices and is still going strong six years later. I encourage you to learn what you can about UNOS and what they do, and donate if you have the wherewithal.
Information is here.
And thank you, from the bottom of my eventually-to-be-reused heart.