My problem with the Big Bang is this: If all the matter in our universe were brought into a very small volume of space, then it would collapse in on itself and form the black hole of all black holes. Nothing can escape from a black hole, especially one so big as to contain everything. Therefore, there could not have been a Big Bang.
Exactly, though some theoretical physicist can probably show you an equation that "proves" that it would blow up at a certain mass.