My hubby and I, right before we go to bed, on Christmas eve open one gift from each other. Typically this is in front of the fireplace with a glass of wine.
We have done this from the beginning. Now with two kids, it's especially important to carve that small amount of time for just the two of us.
For New Years, we have do a "burning bowl" ceremony. You take two pieces of paper and on the first you write everything you don't want to take into the New Year with you (bad habits, debt, relationships, illness,etc) then you burn that piece of paper in a steel bowl (or we use the fireplace).
On the other piece of paper you write all the new things you want in your life in the New Year (health, travel, more time, fun, etc). You keep this paper. And we usually review the last year's keep list during this time. It is amazing how much actually happens! Last year my 8 year old participated, so this will most likely become a family tradition.