Races are filtered as "activities" on your pause menu map but they do NOT show up under the "activities" listing in your info area. However, in the pause menu, it shows up under Diversions - Minigames. It would be nice if they had a list of races and the medals you had won on each one. Instead they just show the # compoleted (but not the total # offered) and then the total number of gold, silver and bronze medals earned across them all.

There are car races, bike races, water races, helicopter races and airplane races.

There are "you against other vehicle" races as well as you-alone time trial races.

Saints Row 2 Walkthrough

Saints Row 2 Review