|You've got a few different ideas a bit scrambled.
The number of spatial dimensions in quantum mechanics is suspected to be 9 or 10 in order to allow construction of a quantum theory of gravity without certain mathematical difficulties. However, that's well short of infinity, and probably not really what you had in mind.
You're probably thinking of the Many Worlds interpretation of quantum mechanics. We usually treat the outcomes of quantum experiments and other quantum processes as being somewhat random, with several possibilities. However, the underlying equations describing how quantum states change have no randomness at all and imply that ALL of the possible outcomes MUST be part of the final state. Different versions of everything, including you's, would develop corresponding to each outcome. Of course, this conclusion is based on the asumption that the underlying equations don't break down somehow. The resulting number of realized possibilities would not have to be infinite, but it would be enormously large.
If that interpretation is correct, then anything you conceive of would be happening in some world, i.e. some part of that overall state, provided that you conceive of things which obey the basic laws of physics.
In trying to decide what interpretation to accept, we're all guessing.
(republished on 07/21/06)