Board Games
Board games are a simple way of gathering dinner party guests and having some quality time together. Ensure that the game is suitable for many players, so you can include all of your guests, or suggest playing in teams rather than individual players. Read the rules of the game out loud -- passing the booklet around so everyone can read it is too time-consuming -- and let the games begin.
Guessing Games
You don't need any equipment for guessing games -- just sufficient space for guests to gather 'round. Twenty Questions is a guessing game in which one player thinks of a specific person and all other guests can ask 20 questions total in a bid to identify her. An alternative is The Famous People Game: trying to describe a famous person without mentioning his name. Each round of such games rarely lasts more than 15 minutes, so everyone can get the chance to pose a challenge to the rest of the dinner party's guests.
Pen-and-Paper Games
Just like guessing games, pen-and-paper games don't require any special equipment. However, these games are more diverse and complicated than guessing games. Such games range from Find the Formula -- a game for math-savvy guests -- to Hangman and your own version of Pictionary. Ensure you provide a surface where guests can lay the paper to write on. A clipboard for each guest can be a costly option, so ensure you can provide a big table, which also has the advantage of bringing guests closer together.
Rock Paper Scissors Tournament
The ultimate activity following dinner can be a tournament that includes all guests but ends up with one undisputed winner. A Rock Paper Scissors tournament is suitable for a large dinner party, as it allows pairs of contestants to play simultaneously, as opposed to darts or billiards tournaments. This way, you avoid the hassle of guests waiting too long for their turn. Rock Paper Scissors is a game that everyone knows how to play and many guests may find nostalgic. And don't forget: prizes for the winners make any game more fun.