My husband's family grew up going to grandma's house for Christmas eve dinner--they ALWAYS had Hawaiian Haystacks. Our family has them on the EVE of Christmas eve. On Christmas eve we have a family party (my side)-exchange gifts and have a white elephant exchange. My kids look forward to it and it's a good time with great food.
Another tradition my brothers and I did was to all sleep in the same room on Christmas eve--my kids have carried this one on--they just visit and giggle and have fun.
We also read from Luke 2 and watch this video:
Traditionally Christmas day my parents also drive to where the grandkids are to see their new "treasures". It's nice because then the kids can show off and visit with their grandparents.
For New Years it's a bit different. A few years in a row we had a Lord of the Ring marathon-eating food and watching the movies together. Last year we missed out for different reasons, my 14 year old is trying to convince the older two it would be FUN! ;)
What are some of your traditions? It's never to late to start one or change one up!