Games that involve making words out of other words include anagrams, and the board game of the same name. Other games, such as Scrabble, use letters from words to make other words.
Anagrams are word puzzles in which the letters of words can be rearranged to form other words. For example, the letters in "Clint Eastwood" can be arranged to spell "Old West action," according to Anagram Genius.
In the board game Anagrams, players try to make words out of a random selection of letters. When a player makes a word it gets placed on the table so others players can see. They then try to "steal" this word by making other words out of it, notes Board Game Geek.
Scrabble is a popular board game in which players set down lettered tiles on a board in order to make words. Players can use words that are already on the board to make words of their own, says Scrabble Site.