Doing the paperwork so that other people can have the useful parts of your body after you're done with it is pretty painless. Most places in the US it's a simple matter of checking the "yes" box next to the question about being an organ donor at the DMV, and then making sure you have the right blurb in your will.
Incidentally, no, paramedics don't check your card and then give up on you quicker or under less stringent circumstances if you're an organ donor. There is no difference in the standard of care for organ donors vs. non-donors. I wish that particular urban legend would die a quick death, but then, I'm not surprised anymore at what people are afraid of without bothering to verify.
Now, being an organ donor is easy, but the paperwork so that the rest of your meat vehicle can be used for scientific research is a fair bit more complicated in many jurisdictions. Whether you want to bequeath your body to a medical school, or to a fuckin' rock-and-roll forensic research facility, or whatever else, it turns out there's all this other extra nonsense about consent and execution of the will and disposition of remains and blah blah blah to worry about.
Which brings to mind the question of why it's okay to do all kinds of science on really old human bodies that we find in caves or inside glaciers or fossilized inside dinosaur turds, despite them being just as human as someone with access to an estate planner and a legally designated executor.
Was there some sort of convention, where experts in science and ethics got together and declared something and then kept it pretty much to themselves? Was genetic and anthropological research divided into a pre-consent and post-consent ethical timeline, and anybody born before some arbitrary date was grandfathered in as pre-consent under the new system?
I mean, personally, I couldn't be bothered to give a shit what gets done with my meat vehicle when I'm done with it, aside from hoping the pieces get used for some last hurrah, but I understand that a lot of other people don't feel that way.
Does the concept of bodily autonomy just go right out the window if you died sufficiently long ago, and/or if your body or its circumstances are sufficiently interesting?
Addendum: Folks have been quick to point out The Kennewick Man and the highly entertaining writeup here on E2 that features his adventures through the American legal system. Unfortunately, that case, and others like it, have nothing to do with the ethics of using a long-dead individual's body in scientific pursuits, and everything about laws meant to appease still-living populations. The court battle over the Kennewick Man was, as they say, "right for the wrong reasons".
In other words, if I give my body to science, ain't nobody give a damn what the rest of my tribe thinks they want done with it instead - just like they can't give away a chunk of my ass for a skin graft if I don't want to sit still for it. Conversely, if I don't give my body to science, (in most places) they aren't allowed to give it away, either.
Indeed, The Kennewick Man had no say in the matter one way or the other, and if those pesky Indians and bureaucrats hadn't intervened, he would have ended up an object of study regardless. In that regard, the case is a brilliant illustration of the question I'm raising with this writeup.