There are many types of jockeys. The most common definition of a jockey would be one who rides atop a Thoroughbred in races, such as the Kentucky Derby. It is also a trademark used for men's underwear.
I have heard numbers from approximately 400-600. The actual number depends on several things. Jockeys have to have a license to compete and the number of licensed riders changes over time. Also, not every person who has a jockey's license actually rides in races, they might be an exercise rider who has a jock's license so they can ride in races three or four times a year. A lot of jockeys who ride regularly are members of the jockey's guild so a good idea of a more accurate number would be counting members of the guild, though there are plenty of riders who are not guild members.
The Rock Jockeys has 80 pages.
Irish Thoroughbred has 189 pages.
About 1050 professionals counting WorldTour Teams and ProContinental. And about 2600 cyclist riding on the professional Tour (Continental).
There are over 50 Thoroughbred racetracks in the USA.
Over 800 thoroughbred trainers in the US.
In thoroughbred breeding stables located in many countries of the world.