Yes. The universe "ends" if by this you mean does it have a boundary. That boundary is not an edge in Space, but an edge in Time. The Universe has only been expanding for a finite time. Thus the physical matter of it has only expanded so far. But more than this, the dimensions of which it is formed (up and down, forwards and backwards, left and right...) have only expanded so far as well. If you want to ask yourself what exists beyond that edge, then ask yourself what exists beyond the South Pole. Or the North Pole. Or any point on the surface of a Sphere. The universe proscribes the directions in which you can travel. The universe contains the directions in which you can travel. You can no more go beyond them than a being walking along the surface of the Earth can go beyond the Earth. Set off in a space ship and travel forever in any straight line and you will arrive back at where you started because the universe does not allow straight lines. Space-time itself is curved.
And if by the Universe "ends" you simply mean that at some point in time it ceases to be, well then either it all starts to fall back in on itself and we get a Big Crunch, or it just keeps on going and going getting thinner and thinner like the atmosphere as you climb a mountain. Eventually all heat and matter is dispersed and there is nothing but cold and lonely molecules hanging in the void.
And if none of that works for you, there's always this: