There are several types of word games such as Scrabble, hangman, and Boggle.

Here is a list of word games you can try out. http://www.wordgames.com/word-games.html If you want, you can also get scrabble. It's a board game and you can play with friends and family.

The list of Games on the related link indicate whether the games have trophies

I've added a related list from Wikipedia for a list of PlayStation games.

There are many math related board games depending on the type of math that is desired. Monopoly, Uno, Stratego, and Yahtzee all use math skills.