That's why it isn't science ;)

Maybe when QM was being developed "collapse" was a debated concept; I'm not too familiar with its history. Currently though, modern QM predicts that ensembles of identically prepared systems select an eigenstate of the linear operator corresponding to whatever observable it is you're measuring. Each of these eigenstates has a probability that can be calculated for it, and the mean value of these measurements is given by <Ψ|A|Ψ>, where A is the operator. I see no implications of collapse with this -- just probabilities of what values you will obtain in experiment.

Not exactly, your statement is correct for single states, however it breaks down for entangled states. When one wavefunction describes two or more particle a measurement on one particle can be thought of collapsing the two particle wavefunction, which then forces the other particle into a well defined state.

Edit, I am not arguing in favour many worlds theory, only that the 'collapse' of the wavefunction is a well developed and useful idea in quantum physics.

Quantum entanglement doesn't seem to be particularly unusual any more so than the fact that electron-electron correlation must be taken into effect when computing energy levels with some kind of QMC. All particles within a quantum system are correlated, so entanglement just kind of falls naturally out of that; I'm not assuming any kind of locality. I suppose what you're saying is that collapse is defined as the process of "fixing" these correlations?