A while back I covered convergence in evolution but I was dealing really with how anatomy can be modified in two or more lineages such that things can closely resemble each other, even when they are not necessarily closely related. However, while of course things can and do convergent evolve, there is a much more simple way that organism can end up looking similar without having to go through all that complex messing about with anatomical changes, you can just get rid of things.
Of course the genetic changes required to, for example, stop generating teeth or lose whole limbs can occur slowly as things are expressed less and less or get smaller and smaller until they vanish, or they can occur swiftly. Even single generations can suddenly be bereft of whole limbs (though of course it will take much longer for this character to spread through a population, even if it is strongly selected for). Still, these dramatic looking changes do come about (think of snakes, various lineages of limb-less lizards and amphibians for example) and of course the similarities (at least superficially, losing a leg is quite dramatic) can be striking.
These kinds of convergences can be harder to detect since by their very nature, they reduce the amount of information available. After all, if a lineage loses a limb then that’s a lot of information that is no longer present to compare to other animals. Until you find an earlier, limbed, relative, spotting what similarities it may have had with other groups (and what it is not similar to) can be tricky. Whales are an obvious example, with the ‘double roller’ joint of the astragalus in the ankle being a key feature in the discussion of whale origins (since it appears in artiodactyls and nothing else) but inevitably is absent in the living taxa what with them not really having hind legs and all, and only the appearance of various fossil forms has helped sort this out.