If you mean a spatial end, the current theory is that it doesn't have one. We believe the universe is not infinite, but that (on the macroscopic level) it may be a four-dimensional hypersphere. If you traveled in a straight line for long enough on Earth, you come back to where you started because the Earth is a sphere. The theory is that if you travel in a straight line through the universe for long enough, you also will come back to where you started (hypothetically).
However, this is far from certain. It's also possible that the universe is infinite and saddle-shaped:
For one thing, we haven't been able to observe enough matter in the universe to provide the gravitational pull necessary to make it spherical. Therefore cosmologists have posited a hypothetical "dark matter" that would make up the difference, and they're looking for it.
These two shapes are not the only ones possible, although they become less probable the more complicated they become. Another possibility is a torus (doughnut) shape.
However, this is far from certain. It's also possible that the universe is infinite and saddle-shaped:
For one thing, we haven't been able to observe enough matter in the universe to provide the gravitational pull necessary to make it spherical. Therefore cosmologists have posited a hypothetical "dark matter" that would make up the difference, and they're looking for it.
These two shapes are not the only ones possible, although they become less probable the more complicated they become. Another possibility is a torus (doughnut) shape.
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