FIA's site (
championships) mentions the following, in strict "FIA order":
FIA Formula One World Championship
FIA World Rally Championship
FIA World Touring Car Championship
FIA GT Championship
CIK-FIA Karting World Championship
Then you have specialized series:
FIA Cross-Country Rally World Cup
FIA International Cup Cross-Country Bajas
FIA Alternative Energies Cup
FIA International Hill Climb Challenge
Not to forget the historic races:
FIA Historic Racing Championships
FIA Historic Rally Championship
FIA Historic Regularity Rallies
FIA Historic Hill Climb Championship
You have european versions of GT3, touring, truck, drag, autocross, rally and hill climb:
FIA GT3 European Championship
FIA European Touring Car Cup
FIA European Truck Racing Championship
FIA European Drag Racing Championship
FIA European Autocross Championship
FIA European Rallycross Championship
FIA European Rally Cups
FIA European Rally Championship
FIA European Hill Climb Championship
FIA European Hill Climb Cup
Finally, rally local cups:
FIA Middle East Rally Championship
FIA African Rally Championship
FIA Asia-Pacific Rally Championship
You can find the regulations there, at FIA's site.