I learned this game from Sharon Grady at the University of Texas. It teaches the concept of rhyme in a fun and active way. I use it with my Kindergarten, First Grade, and Second Grade classes, and sometimes as a reward or time-filler with other students. (They love it, and request it.) It's very simple, but because it deals with rhymes, which can be very complicated indeed if the players are creative enough, it works with just about any age.
Everyone sits in a circle. The teacher says, "I am thinking of a word that rhymes with 'Cat.'" (For instance.)
Anyone who thinks they know the word raises their hand. When called on, they do NOT say the word they think is right. Instead, they go into the center of the circle and pantomime their guess. (In other words, to stick with our example, a child might get into the circle and pantomime "bat" by flapping his arms and swooping.)
The others in the circle try to guess what the child in the center is miming.
The teacher must be careful to explain that even if someone in the circle says the actual word, if that is not what the child in the center is miming, it doesn't count as a correct guess. Once the mime has been guessed, the teacher reveals whether it is the right word. If it is, the round is over and a new word is picked. (With older kids, I let the correct pantomimer pick the new word.) If it is not the right word, another volunteer comes into the circle to act out her guess. Continue until the word has been correctly mimed and the mime correctly guessed.
(In my experience two rhyme sounds presenting especially wide scope for this game are "oat"--boat, coat, goat, float, note, wrote, gloat, moat, tote, etc.--and "air"--bear, wear, stare, stair, chair, where, aware, mare, dare, care, fair, fare, glare, hair, lair, pair, pear, rare, square, tear, etc.)
I'll sometimes substitute this version with very young students who have difficulty with the concept of rhyme. "I'm thinking of a word that begins with 'A.'"
With older or more sophisticated students I'll sometimes play a version of this game in which some theme or connecting idea takes the place of rhyme. For example, "I'm thinking of a person in Revolutionary America." "I'm thinking of something to eat." "I'm thinking of an animal." The connecting concept can be as simple or as subtle as the sophistication of the students allows.