Our family gets together for a big shindig at my parents' [dad and stepmom] house on Christmas Eve. It's great fun for the kids. Not so much for me, cause there's a bunch of them and after a little while, the noise gets to me. Also why I don't like to go to family reunions...but I digress. The years that my daughter stays with me for Christmas, I make her wait until Christmas morning to open her gifts. The years she has to go to her dad's, she gets to open them on Christmas Eve when we get back from my parents'. She doesn't seem to mind either way, as long as it's just the two of us when she opens her gifts. She's a mama's girl, after all. :) Her favorite part of Christmas? Getting to see her Uncle Shawn and eating Grandma's cooking. My stepmom is one amazing cook!
Growing up, I remember my mother was very strict about the only opening gifts on Christmas Day rule. She still is. I thought it was ridiculous then and still do. When you have multiple households to visit, it's unrealistic to try to hit them all on one day, in my opinion, and I see no harm in letting kids open a few gifts early, especially when the kid doesn't visit very often. I still remember one Christmas where my daughter didn't get to open her Christmas gift from my mother until mid-February because of scheduling conflicts. The next year, my mother didn't object at all to her opening gifts on Christmas Eve. Good times!
Bax --- your Easter bunny story slays me. It never occurred to me that the Easter bunny would be vain about his/her tail! Ha!

As a child, I was blessed with magical Christmases.
Usually my brothers and I opened our gifts on Christmas Eve. Then all night we'd listen for Santa to land on our roof and somehow, which was never explained to my satisfaction, pop through our cardboard fireplace and place our gifts around the tree. Fortunately, the colored plastic flames dancing in the breeze of the tiny fan nestled behind the cut-out hearth never did singe Santa's suit.
Christmas mornings were exciting and Santa always knew exactly what we'd like best. I don't think our names were actually on the gifts. We just somehow always knew which gifts were ours.
Well, most of the time. I picked up a really bad habit of peeking from my Aunt Judy. I'd peek in the packages and secretely re-wrap the gifts and hide them under the tree. Apparantely I wasn't as smart as I thought I was because my mom found out. The next year she switched tags and I couldn't figure out for the life of me why my brother was getting a Barbie corvette. It was pink for crying out loud and I wanted it!
Sometimes Santa came early when Dad had to work on Christmas Day. Santa would wait until just the right time, like when Grandma took us into town to look at Christmas lights and sing carols. Getting our gifts early was great, but puzzling. All in all, though, it was not as puzzling as when the Easter Bunny would bring us our own eggs in our own baskets but not hide them because he didn't want to get early morning dew on his fluffy white tail.