I just finished my dissection class about half an hour ago, which is bit of a coincidence...
I've got no problem with donating my body. I'm an organ donor, and will most likely donate my body to medical research as well. It freaks me out a bit knowing that it will have twelve, wide-eyed students, standing around it, cutting it up...but as someone else mentioned, to be placed in the ground and left to rot, or burnt, is too much of a waste.
What comforts me is knowing how respectful and professional the universities/medical schools are. Where I am, the university pays for a private ceremony/service for the family, and there is an annual service at the university to thank the families of the donors. As medical students we're encouraged to attend this.
There are also very strict rules regarding the dissection room. For example, no cameras or mobile phones are allowed in (for obvious reasons). You have to leave them in a locker outside. There are also CCTV cameras.
I read an article recently about a medical school in Taiwan (where donors are scarce due to beliefs about not disturbing cadavers after death), where the students actually learn about the donor's life through visits to meet their families, and take part in a ceremony with the donor's family, before dissection commences. The students form a very close relationship with the donor, and are encouraged to refer to the cadaver as 'teacher', and to thank it. I think it's very interesting to see the cultural differences!
Edit: that was quite a long post. Apologies.