Interesting. I was thinking about this a lot for a while...so much so that i removed my name from the donors list on my driver's license.
I am also going to try and forgo any blood transfusions (if that ever becomes an unfortunate issue).... something in the Bible about "life" being in the blood and whatnot. There are some people that actually think our soul is in the blood, but who knows?
From what I've heard, the blood does not actually become part of your body, it only adds volume to whatever blood is already present, and the foreign cells are eventually excreted through biological processes. They don't stick around. Much the same effect could be had using inert saline solution. Bone marrow is continually producing new blood cells.
"There are some people that actually think our soul is in the blood", please be more specific. That's getting to sound kind of like Jehovah's Witnesses talking.