My dad and I had this issue, and now DD.
My dentist pulled pretty much every one of my baby teeth. He wasn't really interested in whether the pain relief was adequate, so this was pretty awful for me. I think they'd wait until an adult tooth was starting to surface, and bring me in to get the baby counterpart pulled. So most of my teeth didn't get too dramatically out of place, and they ended up straightening out on their own.
My good friend's childhood dentist took the opposite approach:
they let everything grow in, to the point where she had double rows of teeth. Then the baby teeth fell out on their own time, and she had braces for years to fix everything.
DD has had one bottom tooth start to grow in behind the one she had, lost the baby one, and the new one grew right in where it was supposed to. Looks like it's happening again with the other bottom/front.
I don't know yet what we want to do if it happens with all of her teeth the way it did for me...
I started a thread about it here a while back, but didn't get much response... I wish there were more traffic in this forum!