What meats are appropriate for dry-aging
Dry aging creates a certain amount of inherent waste:

The weight of the cut being aged goes down significantly
The outer portions become dry, tough, leathery, may have mold, and are otherwise essentially spoiled and must be cut off

For this reason, it is only really practical to dry age fairly large cuts.  So this would exclude chicken and most fish, and so on even if their meat would benefit.
Tender meats like chicken and fish don't really require dry aging, however, whose main affect is enzymatic tenderization of the meat.   It applies more to red meats, more particularly, beef.
This article at Gizmodo says:

When we create [cool and humid] conditions, we allow enzymes to do their work. And we end up with a complexity of flavor—savoriness, sweetness, some bitterness-that just wasn't there before. There's no cooking method that can generate the depth of flavor of a dry-aged piece of meat.
What happens is that enzymes in the meat's muscle cells begin to break down the meat's proteins, fats, and glycogen—a carbohydrate—into amino acids, fatty acids, and sugars. One amino acid generated by dry-aging—the most important and flavorful one, in fact—is glutamate, which is part of MSG. other amino acids have flavors somewhat similar to MSG; others still are sweet.

So you want a meat whose flavor is strong enough to stand up to, and benefit from, these types of changes.
While not mainstream, one can actually locate dry aged pork, although I am not sure it needs the treatment.  One can even find dry aged lamb!