There's a theory going around the hospitals here. The theory states that if you perform a venipuncture on a kid, the kid will grow up being scared of hospitals. You don't want that, so you avoid it, like the plague. Without any scientific data on this, I'm going to say: bollocks!
I have a theory of my own. It's this: parents get so freaked out about their kids that performing a venipuncture on a kid in the presence of a parent is going to scare the kid. Not because of the venipuncture but because of their parents' reaction.
What do I have to back this up? Absolutely nothing. I can only draw on my personal experience. As a kid, I was frequently (as in many times a year) in the hospital. I had tests taken, I had screws put in my leg and then extracted again, repeatedly. All of this before I was five.
You would think that would make me scared of hospitals, but it didn't. Quite the opposite: I love hospitals. I have a great deal of trust for doctors and nurses. I would attribute part of this to having a nurse as a mom ("Oh, you cut your arm off? Maybe we can just put a plaster on it and see how it feels in the morning").
But I also believe the biggest reason is I've grown used to hospitals from an early age and learned that even if something might hurt momentarily, it doesn't keep hurting. The more you do something, the less scary it will be.
So here's my thinking: if you want to make your kid scared of something, don't ever do it.