It depends on the age, but some good ideas are:

1. Sparklers! Bottle rockets are good for those who are a little older, but of course with some supervision.
2. Watch each time zone ring in the New Year! This is great for all ages, since it doesn't need to be done late at night, and it gives the opportunity for your kids to see what other places around the world look like.
3. Discuss New Year's resolutions with family and friends, and what starting a new year means to starting a new lifestyle.
4. Play games! Board games are definitely a good option (Monopoly can last for hours), but hide-and-seek outside in the dark with some sparklers could be especially fun.
5. Cook some good New Year's themed-cookies, cakes, or anything your kid would be interested in baking. You could even make home-made fortune cookies with New Years-themed fortunes!
6. Turn the New Year into a sleepover - thinking as a kid, that would make the ultimate party. Let them stay up late and watch the ball drop, and then conk out until morning.

Yes! I have thrown many, many kid-friendly New Years parties.

If they are going to stay up until the ball drops, have sparkling cider handy for the toast.

We may think New Years paper tiaras and plastic top hats are dorky. Kids don't!

For the older ones, they'll kill for those snappers - where you pull the string to release the confetti?

Give them their own space. If you have a spare room, throw on a DVD or some music, give them bowls of "gold fish," popcorn, whatever is targeted for kid snacks. While we're downstairs working on the caviar, they would much rather have Fruit Snacks (the kind the squish in your mouth are cool).

Might sound silly, but I had a name tag table set up with the tags, lots of markers, some stickers, and paper for voting best costume. Looked over a bit later, and 4 little girls had taken over, making craft projects out of the name tag table! Good idea. Provide a crafts project, I found.

Beats a babysitter. There may be a few tears here and there, but they'll have a great time at their party within a party. Good luck!!

Many protestant churches have traditional New Year's "watchnight" services which includes a short service, games, a movie, maybe some snacks. Some will celebrate the Lord's Supper and/or eat a meal. It's pretty nice. I'll bet the Catholic Church has services.

Myself? I like sparklers and firecrackers. Horns and shouting and yelling. I like to watch the ball drop. Sometimes I like to go to bed early.