I give blood, so is it possible that people who have had a transfusion could be carrying my DNA?
Not any more. Since scientists found out that BSE can be spread by blood transfusions, they have been ‘leucodepleting’ all transplant blood in the UK. When you give blood, they use a special technique to remove all the white blood cells and leave only the red blood cells, which are safe to transfuse. Human red blood cells don’t have a nucleus (unlike birds) and therefore do not contain any DNA. So transfusions given recently will definitely not contain any of the donors DNA.
In the 60’s, blood was not separated out like this, but we did realise that you could transfer viruses through transfusion like this, so the blood was irradiated. This destroyed the DNA, but left the red blood cells intact.