This comment is old, but I think it indicates a misunderstanding about quantum theory and the MWI so I deemed it worth replying to. I believe the confusion lies in what "World" means, and to whom. In my opinion Everrett's original "Relative-State Formalism" is a much better descriptor of the interpretation, but no matter.

The distinct worlds which are present after a quantum-conditional operation are only distinct worlds according to the perspective of an observer who has engaged in the superposition. To an external observer, the system is still in a single state, albeit a state which is a superposition of "classical" states. For example, consider Schrodinger's cat. What MWI suggests is that quantum superposition extends even to the macroscopic level of an entire cat. However, the evil scientist standing outside the box considers the cat to be in state (Dead + Alive) / sqrt(2), which is a single pure state of the Cat System. Now consider the wavefunction of the universe, which I suppose must exist if we take MWI to its logical end. The universe has many subsystems, each of which may be in superpositions of states according to external observers. But no matter how subsystems might divide into superpositions of states, the overall state of the universe is a single pure state.

In sum: for the universe to "keep track of worlds" requires no more work than for there to exist a wavefunction which describes to state of the universe.

And you can simulate the single worlds interpretation on a computer without running out of resources?

Infinity squared=Infinity, and if the universe is continuous, it can be said (in a mathematical sense), that it takes no more processing power to do one universe than multiples. Besides for the fact that you have to calculate all of the worlds anyway just to get a single world.