I think the important concept here is escape velocity. If you throw a ball into the air, it will come back. If you throw it harder, it will take longer to return, but it still will. Even bullets will fall back to Earth somewhere. However, if you were to fire a bullet at 11.2km/s, it would escape the Earth’s gravitational pull forever (assuming, like most physics experiments that you are working in a vacuum).
When it comes to the mass of the universe, escape velocity becomes a little more tricky because there is no central point that mass gravitates to. Instead we have fragments of matter scattered over much of the universe, and each piece is exerting a gravitational field. Gravity works over infinite distance (qualified of course by the speed of gravity), so matter will never truly escape the gravitational pull of other matter. It is just a question of whether or not escape velocity has been reached – calculated relative to every other piece of matter in the observable universe.
It is my personal opinion that the universe is open, meaning it will expand at ever increasing rates until it reaches a cold death. The oscillating universe theory predicts a Big Crunch. For this to happen, the majority of the matter in the universe must be travelling below escape velocity, and hence be able to be drawn together once again by the force of its own gravity. Gravity will always slow matter, but if the velocity of that matter is large enough it will never slow enough to reverse its direction. If the velocity is small enough, then the matter will eventually collapse into the source of the gravitational field.