Growing up all of the gifts we got at home were from Santa so, of course, we couldn't open them on Christmas Eve as Santa hadn't gotten there yet to deliver the gifts.
I never even knew that other kids got gifts from their parents and, although it sounds strange, I always thought that it was a very selfless thing for my mom to do and it certainly enhanced the "magic" of Christmas. We would go to bed on Christmas Eve with no gifts under the tree and wake up Christmas morning with gifts piled everywhere (in a house with 5 children, even if you each only get a few gifts, it's still quite an impressive mound under the tree). Even now that we're all grown up, all the gifts for us under mom's tree still say "from Santa". It's great!
So, needless to say, I'm a big fan of opening gifts on Christmas morning. I even sneak up in the middle of the night to put DH's gifts under the tree (partly because of tradition and partly because he's such a big snoop that he'd never leave the gifts alone if I put them under there any earlier!) and fill his stocking.
DH, on the other hand, would prefer to open gifts Christmas Eve because he's like a kid when it comes to presents. So far, I'm winning the battle but every year he tries to wear me down!