They can take any and every organ or individual part they need. Even for your hard-drinking, -drugging, heavy-smoking types, you'd be surprised what they can use. Bones, bone marrow, corneas, skin, heart valves (maybe). They can use more of your internal organs when you die young and healthy, say from a quick ruptured aneurysm or a motorcycle accident head-injury, than when you die of ripe old age.
I don't plan to donate my entire body to medical science. I have no illusions about that, although I appreciate the folks who supplied themselves as cadavers for my first-year anatomy/physiology class in med school this year. The "research" that's done is crude dissection and examination by a bunch of medical noobs. Those donated bodies don't enhance hopes for a cure for cancer or other diseases. They let first-year med students look at musculo-skeletal systems, livers, lungs, hearts, blood vessels, and pancreases, among other things. It's a necessary thing, but it's not very dignified.