Here's a list of some tyres and their manufacturers:-
Michelin - France
Worlds number one tyre manufacturer. Own the brands Michelin, BF Goodrich, Kleber, Uniroyal* and Riken.
Bridgestone - Japan
One of the original big three. Own the brands Bridgestone, Firestone, Daytona and Europa.
Goodyear Dunlop - USA
Goodyear recently merged with Dunlop to form one of the largest tyre manufacturers in the world. Own the brands Dunlop, Goodyear, Fulda, Falken and Kelly.
Yokohama - Japanese
A brand in themselves, Yokohama claim to be the 7th biggest manufacturer in the world.
Pirelli - Italy
Pirelli claim to be the 5th largest tyre manufacturer in the world. Most of it's retail is through the Pirelli brand but have more recently released the Ceat and Courier brands.
Cooper Tyre - USA
Cooper recently bought the Avon brand. They now own Cooper, Avon and Mastercraft.
Continental - Germany
Owns Continental, Uniroyal*, General Tyre, Gislaved and Semperit.
Toyo - Japan
Toyo are one of the newer budget performance tyres to market. Formed many partnerships around the globe.
Kumho - Korea
Kumho is also a budget road tyre with a strong sporting range.
Vredestein - Netherlands
* To add to confusion Uniroyal is Continental owned in Europe and Michelin owned in USA