In our family it's always been traditional to start opening a few presents a day or two before Christmas, with the majority opened on Christmas Eve. Originally this was somewhat out of necessity, because we would often travel to the grandparents a day or two before Christmas and just couldn't fit all the kids' presents in the car. But also, by spreading Christmas out a bit, I think it gave the kids time to appreciate each gift a bit more, and opening on Christmas Eve means you don't have kids that can't go to sleep and then parents being awakened at the crack of dawn, and then having to travel to relatives on Christmas Day in a sleep-deprived state.
Now I know someone is probably going to ask how we pulled that off, since "Santa" supposedly comes on Christmas Eve. Well, the fact is that we always treated Santa and the Easter Bunny and the Tooth Fairy as "pretend" characters, just like all the other characters on TV. We just never felt that it was right to lie to kids about Santa Claus, and then pull the rug out from under them as they got older. We also had to explain, once they were old enough for kindergarten, that some of their classmates believed Santa was a real person and that it wasn't nice to try and correct them, that they would figure it out on their own in two or three years (now that I think about it, that could be an early lesson in tolerance for the beliefs of others, thought at that time we probably didn't think about that). And yes, there were one or two people in our family that thought that it was horrible that we didn't lie to our kids about Santa (which is something I just couldn't wrap my head around - since when did lying to small children become such a cherished value?) but the thing is, we didn't shield our kids from all the Santa stuff, they heard "The Night Before Christmas" and all that, but we just never tried to pass off Santa as being a real person, or anything more than a fun pretend character associated with the holiday season. And that really made the holidays a lot less awkward, except for the one or two relatives that just couldn't believe we'd do that!