This is an excruciatingly simple game that can be played in classes that are very young or quite advanced. To play, the teacher first says a word (such as "apple").  The next student must then say a word that begins with the last letter of apple, such as egg.  The last letter in egg is G, so the next student must say a word that begins with G, and so on, and so on, and so on. A typical string of words looks something like this:

apple - egg - ghost - table - eat - take - eleven - night - two

You can simply take turns, going around the room, or have them stand in a circle and sit down if they are wrong. Also, I sometimes have them play in two teams: I write 1 - 10 on the board for each team, and they make a line at the back of the room and take turns, one at a time for each team, running to the front to write ONE WORD.  The first team to finish wins, and gets a frilly super stamp or whatever floats their boat.

It's important to stress, however, that they cannot repeat the same word twice.  Otherwise they may end up in one of these ESL Cartesian loops: elephant - table - elephant - table - elephant - table - elephant - table - elephant - table...

To make this game more interesting and challenging for more advanced students: limit words to a certain category, to force them to think and be more creative.  Examples of useful (and tested) categories include: nouns, verbs, adjectives, English names, animals, foods, drinks, something big, something small, something noisy, something ugly, etc.