Balderdash, Scattegories and Catch Phrase are a few funny board games to play in groups. Pictionary and charades are some other funny games that only require writing utensils, some paper and people to play.
In Balderdash, players make up a definition to an obscure word. The round leader then reads the made-up definitions along with the real one, and the players guess which is the actual definition. The resulting made-up definitions are often amusing or more convincing than the true definition. Catch Phrase and Scattergories are games that involve fast-talking and thinking, which often results in hilarious statements and exchanges between players.
Groups also have fun playing charades. One team writes suggestions for a player on the other team to act out, and other players on the second team have to guess the action. Pictionary is similar, but the players draw, instead of act-out, the suggestion.