How many different types of cheese are there in the world?

According to the rind, there are 7 types:

1. Fresh Cheeses: Banon, Ricotta, Feta, Cottage cheese, Cream cheese, etc...
2. Natural Rind: Sancerre, Chabichou, Crottin de Chavignol, etc...
3. Soft White Cheese: Camembert, Brie, Chevre Log, etc...
4. Semi-Soft: Edam, Pont L'Eveque, St Nectaire, Tomme de Savoie, Langres, Carre de L'Est, Epoisses, etc..
5. Hard Cheeses: Cheddar, Parmigiano Reggiano, Gruyere, Manchego, etc...
6. Blue Cheeses: Stilton, Roquefort, Gorgonzola, Maytag Blue, Cashel Blue, etc...
7. Flavoured Cheeses: Cornish Yarg, Gouda with Cumin, Stilton with Apricots, Devon Garland, etc...

There might be more types, but this are the most known.

(source [thecheeseweb.com])Link no longer exists
https://en.wikipedia.org/wiki/Types_of_cheese

A bunch...To name a few:

American
Asiago
Blue
Brick
Brie
Camembert
Cheddar
Colby
Colby Jack
Cottage Cheese
Dry Jack
Edam
Farmer Cheese
Feta
Fontina
Gorgonzola
Gouda
Gruyère
Havarti
Kasseri
Limburger
Mascarpone
Monterey Jack
Mozzarella
Muenster
Neufchâtel
Parmesan
Pepato
Pepper Jack
Port du Salut
Provolone
Queso Blanco
Ricotta
Romano
Scamorza
Swiss
Teleme

http://ilovecheese.com/cheeses.asp?Search=Q-Z

The website Wisconsin Cheese states that there are more than 1,800 different types of cheese in the world. The site classifies cheese by 6 main criteria:

* Milk. Different types of cheese are made from the milk of cows, goats, sheep, or buffalo, or combinations of each.
* Country or region. Many different types of cheese are named after or associated with the place they were first made. Parmesan cheese, for example, originates from the area around Parma, Italy. Gouda was first traded in the Dutch town of Gouda. And cheddar cheese originated in the English village of Cheddar in Somerset. One of our state's favorites, Colby, originated in Colby, Wisconsin.
* Age. Fresh cheese is intended to be eaten right away while other cheeses may be aged from a few months to a few years or more.
* Texture. Cheese is often categorized by its texture, from soft to semi-soft and semi-firm to hard. Generally, the longer a cheese is aged, the lower its moisture content and the harder it becomes.
* Flavor. Cheese is often described as having flavors that runs from mild to extra sharp. Mild cheeses tend to be younger cheeses, while stronger flavored cheeses tend to be aged cheeses or cheeses with mold or bacteria cultures introduced during the cheesemaking process.
* Preparation. Many young cheeses are unripened, meaning they have no additional added cultures. Mold-ripened cheese like blue cheese or washed-rind cheeses like limburger have different mold or bacteria cultures introduced during the cheesemaking process that helps develop stronger flavor. Pasta filata cheeses are stretched during the cheesemaking process to produce a stringy, chewy texture like mozzarella.

https://www.wisconsincheese.com/about-cheese/different-types-of-cheese