Musical Red Light Green Light
This game is a little like red light green light, but instead of announcing whether they are allowed to move or not, they have to move to the beat of the music. Begin by showing your children how to count the beat of the song, which is best done by having them clap along to identify the tempo. The goal of the game is to walk to the beat, and then freeze when the music stops. If you walk on an offbeat or when the music stops, you have to go back to start. The goal is to get across the room to the conductor who controls the music. You can easily adjust your tempo to play faster songs by simply counting, and clapping on the 2 and 4 beat of any 4/4 signature song.
Drum Karaoke
This game is great for teaching abstract beats as it can be played to nearly any song. This game is basically karaoke, but instead of singing along to a given song, you drum along. This game is great for kids because not only do they love to hit thing with wooden sticks, it is also a way to instill a sense of rhythm, teaching them to follow along to the tempo and in different time signatures. The game works best if you allow the kids a chance to practice through their song a few times until they understand the beat, and then have them go to town on it, trying not to make any mistakes.
Sequence
This game is simple, but it's a lot of fun, especially for younger kids. Count off your kids, assigning each a number in sequential order. For younger kids, you can line them up and just count them off in increments of ones, as it will be easier for them to keep up with the rhythm this way. Start with a very slow rhythm, then either clap to the beat or set a metronome so everyone can keep tempo. The game is played by each person saying their number on the beat and trying to get from the first person to the last without anyone missing their beat. This is a fairly simple game when the rhythm is slow and everyone is in order but when you start speeding up the tempo it can get pretty difficult. On top of that, you can turn it in to a math game and have people represent increments of 2 or 3 or whatever and they not only have to keep track of tempo but where they stand within sequential order.