You mean the Many-Worlds interpretation? That's not every choice, but every quantum measurement. And it's not necessarily an infinite number. And it's not a theory, but an interpretation. And it's actually very Occam's Razor-ish (at least that's what proponents claim), because it needs less postulates than the standard Copenhagen interpretation. The many worlds are a consequence, not a postulate.

It's the multiverse theory, typically discussed under the framework of string theory.