Starting in 2005, children conceived with donor sperm or eggs will be able to track down the donor. According to an article from BBC News, the new law will allow 18-year-olds to find out who the donors are.
The new law doesn't change the treatment for sperm or eggs already donated, except that recipients will be allowed to know a little more descriptive information (eye color, hair color, occupation, and religion) for the time being.
The key concern on the privacy side is that donor clinics will get fewer donations and thus reduce the options for infertile couples who would usually require a donor.
However, I found more interesting the idea of comparing the privacy issue to the privacy issues of adoption. I understand this from the perspective of the child, since there is a similar bond (or lack thereof) to the birth parents in adoption and donation. However, it does seem that the circumstances differ a bit from the perspective of the donor vs. the parents giving a child up for adoption.