A New Year's Eve party is the best time to play games, even if the event is an adults-only affair. Pick games that connect to New Year's thematically. For example, make a game based on guest's resolutions or a game featuring trivia about the previous year. While these games are targeted at adults, any teenagers or children at the party may want to get in on the fun too.
Go through magazines or newspapers from the previous year. Clip pictures or stories from the magazines that were memorable, such as a famous wedding or a famous actor doing something ridiculous. Hide all references to a date on the clipping. Ask guests to guess the month or general time period during which the event occurred. Choose both common, well-known events as well as more obscure ones to make the game challenging. The guest who gets the most right can win a calendar for the New Year. Alternatively, the guest who gets the most wrong can also win a calendar for the upcoming year. Stick with light-hearted events, instead of major tragedies, to keep a festive atmosphere.
When guests arrive at the party, have each one write out a resolution or two on a slip of paper. Place each slip into a hat. The resolutions from each guest should be real ones. Write a few fake ones down too. Throughout the party, pick each resolution out of the hat and read it out loud. Guests should attempt to guess which resolution belongs to which guest and which resolutions are fakes. Give prizes to the guest who guesses the most correctly and to the guest with the most unusual resolution.
Pick themes that relate to New Year's for a game of charades, during which guests must act out the themes, or for a game of Pictionary, during which they must draw the themes. Themes that work include events from the previous year or more general themes that have to do with time, such as "back to the future" or "time of your life." Divide the guests into two teams. One player from each team goes at the same time, drawing or acting out the same idea. The team that guesses the most correctly first, wins. If you want, give the teams the option of either drawing or acting out the idea during each round.
Find images from news or entertainment stories from the previous year. Each image should have two people in it who are somehow connected or a person with an object. For example, cut out an image of Prince William and Kate, then cut that image into two pieces, one of William and one of Kate. Tape half of each picture onto the backs of guests as they come in. Guests have to guess who is on their back and find their partner. Don't limit yourself to couples, for example, you can have a group of three or a picture of a person with something they invented that year.