What are the levels of brown belts in karate?

There are scores of karate styles, most of them offshoots of other styles of karate. The primary styles as recognized by the World Karate Federation for form exercises are:

Shotokan-ryu

Shito-ryu

Budokan

Kyokushinkai

Gojo-ryu

Wado-ryu

Shorin-ryu

Uechi-ryu

Almost all other styles are influenced by one or more of these. If you're curious, Chuck Norris has an 8th degree black belt in Tai Kwon do.