Solid axles (aka spools) are sometimes used in on-road racing instead of a differential. They are be used in the front or the rear, depending on the type of racing.
Using a solid axle rather than a differential forces the left and right wheels to turn at exactly the same speed. Due to their simplicity, they are lighter than differentials.
Using a spool in the front reduces weight, but reduces steering response and cornering speed.
See more about differentials.