Wikipedia's article on antimatter says this:
There is considerable speculation as to why the observable universe is composed almost entirely of ordinary matter, as opposed to a more even mixture of matter and antimatter.
And on antihydrogen:
For example, excited antihydrogen atoms are expected to glow the same color as regular hydrogen. Antihydrogen atoms should be attracted to other matter or antimatter gravitationally with a force of the same magnitude that ordinary hydrogen atoms experience. This would not be true if antimatter has negative gravitational mass, which is considered highly unlikely, though not yet empirically disproven (see gravitational interaction of antimatter).
If antimatter had negative mass and generally repelled matter in large quantities that had little other forces acting them, we could have vast "pockets" of antimatter and matter peacefully coexisting, repelling one another. In fact, if antimatter looks the same "color" as matter and all we have to look at in deep space is light, for the most part, then we could have "anti-galaxies" that look the same as ordinary galaxies. It seems this idea has been considered, as Wikipedia notes:
Antimatter may exist in relatively large amounts in far-away galaxies due to cosmic inflation in the primordial time of the universe. Antimatter galaxies, if they exist, are expected to have the same chemistry and absorption and emission spectra as normal-matter galaxies, and their astronomical objects would be observationally identical, making them difficult to distinguish. NASA is trying to determine if such galaxies exist by looking for X-ray and gamma-ray signatures of annihilation events in colliding superclusters.
How would we know, in this case, that some of the galaxies we see aren't "anti-galaxies?"
Based on what I know, the thing that doesn't add up with anti-gravity is this:
Light is affected by gravity. If anti-matter's gravity is negative, then either (1) light only cares about the magnitude of gravity and is attracted to anti-matter or (2) light is repulsed by antimatter.
This would be weird that light "acts" like "matter" in that it's attracted to matter and but also like "antimatter" in that it's attracted to "antimatter". A is attracted to B. B is attracted to C. A is not attracted to C. That's weird.
This sounds like it could be related to dark matter.
See also arguments on Wikipedia's article on regions of the universe where antimatter dominates.
Another question addresses the issue of antimatter galaxies, but it does not consider the possibility of antimatter having negative mass.
There are (2) positively scoring answers on that question (which assumes the following: a star composed of antimatter hydrogen would fuse to anti-helium in an analogous way to our own Sun, and it would emit light and radiation at the same wavelengths as any regular matter star and would cause the same gravitational forces):
First positively-scoring answer:
This argument assumes that antimatter and matter regions would be close enough or connected such that annihilation would be visible. If we assume that antimatter and matter regions are gravitationally attracted to one another, like the question assumes, then this answer makes sense. My question assumes the opposite - that antimatter gravitationally repulses matter and vice-versa. Therefore the thin inter-galatic medium strands connecting gravitationally bound filaments might not exist between antimatter and matter (anymore - they've been annihilated, causing an actual void, or at least the visible appearance of one).
Here is what the second positive-scoring answer has to say:
This answer admits that "the telltale sign would come from supernova neutrinos, although at present we can only detect such neutrinos from nearby galaxies". The absence of anti-neutrino emissions (today's measurements) would only imply that "nearby galaxies" are not anti-matter. What about galaxies that we can see that aren't nearby? This answer doesn't address those.