I have a son by my first marriage, and both a daughter and son by my current marriage.
I have also had a vasectomy.
Losing contact with the children you formed and led and taught and laughed with... My god that hurts.
With the relationship, at least you can be pretty sure when that is over. The signs are usually pretty clear to everyone involved. You can't divorce your kids, though.
One of the only reasons my wife an I are still trying to "work things out" is because of the children. I don't want to hurt my daughter, who is four years old, by leaving. She wouldn't understand at all why Daddy isn't coming home anymore. My son, 18 months old right now, would just be confused. How could I explain the terror of never being able to hold him close to me in the mornings when I wake him in his crib? How could I describe the joy that a big, sloppy, open mouthed baby kiss gives me?
How can I tell another woman, if I ever meet one, that I will never be able to give her a child, a child that I know I will love and cherish more than my own life?
Kielle's points are all TRUE.
But the worst part about divorce is losing those smiles...
Update:
pimephalis is right, and I did leave out that part. My parents divorced when I was five, and it is very difficult for the children in that situation as well.