There is a more comprehensive New Years Party Games list, but on this page I just wanted to list my absolute favorites.
Since the evening is all about looking back a bit and rolling in the new, my favorites have to do with what went on during the year and a little about what might be coming. That is why you will only find games on my favorites list that deal with these subjects. All the games I posted on the other page are great games, don't get me wrong. But when I want to stick to the theme of New Year's, I stay with this list.
New Years Eve events tend to end later than quite a few other events, so conventional entertainment choices, including dancing, may perhaps not be sufficient to keep your guests entertained all night. That is why I recommend spacing a few of these out during the whole evening. Take some time between games to eat, mingle and get to know the other guests. Then call everyone back for another round of fun.
I would also have prizes for each game. The more games, the more prizes or favors you will need. This means more people will win. Sometimes, your guests will have been invited to several parties and they need to attend more than one. By playing a couple games, and maybe winning a prize, they can feel comfortable enough to sneak out before the clock strikes mid-night.
Remember to keep it safe. Make sure everyone has a designated driver for the evening if they will be traveling home. Most cities have a couple free services for the night. Check with your local police station to see if your city participates in any of these services.