You can use a negative value of jump boost effect to achieve a corrupted jump boost (which, in effect, makes an entity unable to jump). You can't use the /effect command to do this, though, you have to edit the entity data manually. Which can be done like so:
/entitydata @e[type=EntityHorse] {ActiveEffects:[{Id:8,Amplifier:-128,Duration:600,Ambient:0}]}
Where Duration is measured in ticks. So 600 ticks will give you around 30 seconds of no jumping. Adjust this value depending on what you want. This is the best solution if you want just a temporary "no jump" effect.
If you want this to be permanent, that can be done too. Horses also have a horse.jumpStrength attribute in their NBT data. If you want to make all horses unable to jump, you can change that value to '0' with the following command:
/entitydata @e[type=EntityHorse] {Attributes:[{Name:"horse.jumpStrength",Base:0}]}
This will make all horses completely unable to jump. You can reset this by setting the value to some other value, however, that will set the overall jump strength for all horses to be the same, which may or may not be what you want.
I don't know why so many players say this isn't possible. In fact, it is simple!
Just enter this command into a command block:
/summon Wolf ~ ~1 ~ {Owner:Notch}
Of course, the name Notch could be replaced with the player's name that you wanted to have it tamed to. @p does not work! (The command will generate a tamed wolf one block above the command block, tamed to the person of your liking.)
Best Answer
The command for getting rid of all effects is
/effect *player* clear, so if you put a pressure plate or something on the finish line connected to a command block, the block command would beeffect @p clear. If however your racers have other effects that you don't want to remove, useeffect @p 2 0, which will remove slowness only.