Make a "racetrack" with six lanes. You can make a sturdy track out of wood and paint the lanes on, or just use a long sheet of the wide paper used to cover bulletin boards and draw the lanes on with a marking pen. Divide each lane into about 8-12 spaces, as shown below. 

You can have up to six players at one time with this game. The player places their horse (or vehicle, animal, etc.) on a lane. The operator throws a die (the jumbo foam ones work well for this) and the player whose lane number comes up gets to move forward one space.

You can also use a pair of dice, one to determine the lane that moves and the other how many spaces to move.  The first player to the finish line gets a prize.

Space Race: Use spaceships as the vehicles and paint stars on the track.

Start Your Engines: Use mini cars, such as Hot Wheels, and paint the finish area like a checkered flag.

Elephant Walk: Use plastic elephants and paint the course like a circus ring.

Bug Racing: Use die cast Volkswagon Beetles as the vehicles.

Steeplechase: Use plastic horses and put "jumps" between the spaces. Ideas for building jumps include Legos, building blocks, Kinex, painted dowels, tree twigs, etc.

Bring Home the Bacon / Pork Chop Speedway: An alternate way to race with battery operated pigs. You just turn them on, lift the barrier, and first pig to the finish wins.
See the Links below for an example.