IANA physicist, but my layman's understanding was that under many-worlds the universe doesn't actually fork. Rather, the superposition of states observed in things like the double-slit experiment applies to all particles all the time, including the ones in our brains. When we observe a system undergo an apparent collapse of the wave-function, what's actually happening is that we/our brains have become entangled with that system, so each of our brains' states becomes correlated to one of the system's states. To a consciousness generated by one of those brain states, it appears that the system under observation has undergone a collapse; however, the result of that collapse appears different to each such brain state.

At least, that's what I took away from this:

http://www.askamathematician.com/2010/10/q-copenhagen-or-man...

and this:

http://www.askamathematician.com/2011/11/q-according-to-the-...