How many types..

lots, but one one can be the best and that is New York Audio Labs, too bad they went out of business when i was like 10

Do you mean brands?

Atma-Sphere
Joule Electra
Tenor (they went out of business, not sure if they're back)
Berning (a point of contention since some claim it's not a true OTL)

There are several others by companies that are defunct.

Brian

Add Transcendant to the list.

Silvaweld, Graaf and Croft are three more.

Generally OTLs seem to split along two lines: Symettrical circuitry, using a Circlotron for an output circuit, and Asymettrical, using a Totem Pole output, which looks a bit like a mu-follower circuit.

OTLs may or may not have an output coupling capacitor. Totem-Pole types usually use negative feedback, although there is at least one patent where the amplifier did not use any.

In Circlotron OTLs, negative feedback is entirely optional.

Either can be any combination of triode, tetrode or pentode, and class A, AB or B.