No one likes needles..
I had to have a blood test recently, and it gave me alot of confidence that the guy before me caused a massive delay because he bled alot more than supposed to and passed out.
We in the waiting room saw people running about with fans, etc...
It went alright though. As long as the doctor/nurse or whatever is careful enough, you shouldn't have any damage or loss of blood due to it. But I guess anyone can slip, etc if peopel are really scared and shaking, etc, which causes more harm in the long run.
If you stay still etc, theres alot less that can go wrong.
Just close your eyes is all I can say.