Start by removing the non-ball ornaments, which are usually the most sentimental. Tell stories as you wrap each ornament. If you're undecorating with kids, make a game of finding each ornament as you describe them. This won't make taking down the tree quick, but that's the point -- you're making it enjoyable instead.
If you invite guests, make personalized ornaments (this can be as simple as buying a box of ball ornaments -- on sale after Christmas -- and writing a name on each with a paint pen). When guests find their ornaments on the tree, they can take the down and keep them as a party favor for next year.
Get outside, and make taking down the outdoor decoartions a group effort. With hot chocolate waiting, of course!
Leave the snowmen and other decoartions that say winter, but not necessarily Christmas, on display to keep a little whimsy after the holidays. Nativity scenes traditionally stay up until Epiphany on January 6.
Use up leftover champagne from the New Year's Eve party (or buy an extra "undecorating" bottle in adavnce) to make refreshing mimosas for the adults. No fancy mixing is required -- just mix half orange juice and half sparkling wine. For non-alcoholic mimosas, use sparling water.
Serve lucky food in a buffet-style sit down meal. Hoppin' John, pork and sauerkraut, lentils, fish, round fruits and osechi are some traditional good luck foods from around the world. If your family doesn't have a lucky New Year's meal yet, start the tradition. Mix it up -- serving several lucky dishes may make an odd combination, but that's part of the fun. If you you're less ambitious, pick one and find a great recipe for it.