Do we ever see a wormhole in Star Trek that goes beyond our galaxy? Wormholes are able to cross great distances, but I don't recall ever seeing one that emerged anywhere else.
No. We never see a wormhole that goes outside of the Galaxy. Given the science behind the concept of the Einstein-Rosen bridge, it should be theoretically possible if someone were to find and create a link between the two locations. But using the science as we understand it, stable wormholes are difficult to conceive of without an outside energy source keeping the link between the two locations.
It is difficult to be able to answer that question with any clarity since we don't have a large sample of wormholes to work from. But from the very limited sample we can say, yes, wormholes in the Star Trek universe do not tend to exist outside of the galaxy proper.
As far as the Federation is concerned there are no naturally occurring wormholes that are actually large enough for a ship to pass through. Wormhole theory have been examined in the Federation and micro-wormholes have been used to send datasignals through space and time. Voyager uses a wormhole to send messages to the Alpha quadrant but the messages ended up being sent through time to a Romulan vessel. (VOY: "Eye of the Needle")
Wormhole theory in the Federation recognizes them as potential portals through time but no naturally holes have been large enough to use for more than communications.
No known naturally-occurring stable wormholes had yet been discovered in the Alpha or Beta Quadrants. The only likely candidate, the Barzan wormhole, was found to be unstable at its far terminus. However, several relatively stable wormhole-like phenomena have been reported in the Delta Quadrant. (TNG: "The Price"; VOY: "Eye of the Needle", "Night", "Counterpoint") -- Memory Alpha
It's hard to come up with a coherent answer when the series is so inconsistent about the size of the reachable universe; traveling across a large fraction of the size of the galaxy goes from taking mere hours (ST: The Final Frontier) to tens of decades (Voyager).
I believe it is implied, but never explicitly said, that the whole franchise occurs within the Milky Way (barring trans-dimensional stories), so the answer is probably "no".
While not a scientific answer, they may have been blocked by the Q in order to keep 0 out of the galaxy.