Chao Races are probably what you raise your Chao for. They test its abilities and eachr ace focuses on one attribute. You can encourage your chao by pressing A or B to give it a temporary boom of speed. But if you do so Chao's stamina falls much faster. Once the bar is empty the Chao slows down damatically. When you enter the race first only the four Beginner Races will be availabe. Win all of them to unlock Jewel Race and Challenge Race. To get Dark Race and Hero Race you must have raised both a hero and a dark Chao. In each of them your Chao can win toys and medals and you can win the missing emblems. For more about toys go here.
Note: Only dark Chao can race "Dark Race" and only hero Chao can race "Hero Race"

..:: Beginners Race ::..

This is the perfect start for your Chao in racing. Each of the four courses has three difficulty levels. The Chao racing against you become faster from level to level. Win level three of a course to get an emblem and a toy for your Chao.
Each course focuses on a certain ability:
Crab Pool Stump Valley Mushroom Forest Block Canyon
Swimming Flying Running Power

..:: Jewel Race ::..

Here you get 6 different courses and 6 levels each. They're much longer and more difficult. You need more than just one ability, but they still focus on different attributes. You win a toy after each 6th level. Emblems appear "randomly"
Aquamarine Topaz Peridot Garnet
Swimming Flying Running Strength
Onyx Diamond
Intelligence and Luck Everything

..:: Challenge Race ::..

This is the most exciting race. You have 12 different races and race against the most funny Chao/Animals/Whatever. But it's pretty hard and you can only win a toy every 4th race. Appearently there are no levels in this one and you need all abilities everywhere. Just enjoy it, that's what it's made for!
Challenge! He returns. I'm trying! Small Animals Horrible! Oh, my egg!
Race against the stong Gold and Silver Chao. Race against Chaclon, the super Chao from SA. Omochao race! Ever dreamt about racing against the little animals you've collected? Race against a group of Cockroach Chao! Wee! Walking eggs! I wonder how they can run so fast.
Be afraid! Be afraid! Be afraid! He strikes back. Kid's Troops Ultimate Rival
Ah! Skeleton Chao! A whole group! Is it halloween already? Chao with a Pumkin head! No!! Ghost Chao! Chaclons revenge race. Now he's even faster! Chao Ranger! Chao in all colors! Meet the Light Chaos Chao, he's really fast!

..:: Hero Race ::..

This race is sure strange! What do you expect a hero race to be? Hero Garden design, Angel Chao everywhere... right? Wrong! You get creepy music, dark garden design, and you race against Dark Chao. But your own Dark Chao can't enter. That's how it got the name -.-  There are four different races and you can get 2 toys for the Hero Garden.
  Baby Devil Child Devil Death Troops Devil vs Angel  
  Race against Dark Baby Chao Race agaist normal Dark Chao Dark Chao with a Skeleton Head Race against the Devil Chao  

..:: Dark Race ::..

Same thing with this garden. It's all shiny and you gotta race against Hero Chao. Again there are four courses and you get two toys for the Dark Garden this time. Hero Chao cannot enter.
  Baby Angel Angels Flying Angels Angel vs Devil  
  Race against Hero Baby Chao Race against normal Hero Chao Hero Chao with bird wings, prettyfull ^_^ Race against the Angel Chao  

..:: Party Race ::..

Just as the name says, it's more like a party than a race. This time only YOUR Chao will race! Select up to 8 Chao from the Gardens or Memory Card to race against each other. Invite a friend to challenge your best Chao! You can choose from 10 different courses you already know (the beginners and jewel courses), you get no emblems and no toys. It's just for fun!