Are there any examples of animals which have evolved similar traits but via different...

...evolutionary lines? Of course, evolution happens over a long period of time from what I've been told, so I'm sure this is probably all theoretical, but I'm curious if there have been any different species that have almost seemed to "converge" as opposed to branch out. An example of what I mean to say is that, I was reading on http://www.posterlovers.com/animals/bats.htm that there is some "morphological evidence that [some bats] evolved flight separately from [another suborder of bats]". Though I'm not certain what precisely they might mean by "separately", I was curious as to whether or not there are more definitive and pronounced examples of two different species of animals independently evolving similar traits. The way I assumed things, I was under the impression that evolution generally branches out to culminate different varieties of a same general species. Are there specific examples of two different species evolving to be more similar?
 
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