What are all the bases?

[cjbnc]

How many "real" bases are there?
It cannot include ones that change their proportion, as the case of Montroll's dog base.

Origami Design Secrets by Robert Lang has an extensive discussion in Chapter 4 - Traditional Bases.

Quoted from his website glossary at: http://www.langorigami.com/info/glossary.php4

Classic Bases: the four bases of antiquity (Kite, Fish, Bird, and Frog) that are related by a common structure.

Standard bases: the most common origami bases, usually taken to include the Classic Bases plus the Windmill Base, Cupboard Base, Preliminary Fold, and Waterbomb Base.

[David]

Disagree with Dr Lang, but that is not new

A base should be more than two raw edges folded to the centre, so no kite or cupboard ones in my glossary.

So the basic forms are the preliminary, waterbomb and the fish base ( similar number of folds)

As I mentioned earlier the bird base and the frog base are progressions of the preliminary base.

Lots of creators have there own starting points, who has heard of Fred Rohm's "Simplex Base" (Origami 2 Rob Harbin 1971) or Elias Animal Base? they are just not in general use.
In Origami Omnibus (Kasahara 1988) there is a whole chapter using a common starting point, but he does not call up the "windmill base".
There have also been a lot of creators, Edwin Corrie springs to mind, who designed avoiding bases.

So I think in answer to the original post, I would find and fold as much as you can find, do not dismiss the early publications- take a look at Secrets of Origami (Harbin 1971) He talks about preliminary fold , and bird base.
Many books will have a common starting point but rarely "a base"