Convergence and its importance has been covered on here before, with examples of structures being lost as well as gained or altered. One of the most striking examples is the loss of teeth in the ornithodirans (that is, pterosaurs and dinosaurs and a few others).
Teeth can of course be adapted to do all kinds of things, but they can be expensive to produce and maintain (energetically) and they are not always the best tool for a job (and in terms of pterosaurs and birds are relatively heavy structures too) so you can see why some clades might loose them. And loose them they do, pterosaurs did it at least twice (and perhaps three or four times depending on exactly which phylogeny you prefer) and in the theropods there are ceratosaurs, ornithomimosaurs, oviraptorosaurs and birds (themselves more than once) all producing toothless forms. I don’t think there are any toothless sauropods or ornithischians, but several clades of the latter at least gave up teeth in the premaxilla. It’s not quite the same thing, but you could argue that they at least lost teeth from the bones of one part of the skull, if not lost their teeth entirely. It’s quite a record – at least eight independent sets of tooth loss which for a clade that are often characterised as being toothy shows just how often, and how easily, teeth can be lost.
(And indeed that’s just ornithodires there are several other archosaur and reptile clades that produced toothless forms, most obviously of course, the tutles).