The (sadly extinct) Tasmanian Tiger and living wolves provide an excellent example of convergent evolution. They have the same ecological niche, with the Tiger filling the role of a top predator in Australia, while wolves are found throughout the northern hemisphere. But the Tiger is a marsupial, while wolves are placental mammals.
Creationists would argue that this is evidence of common design, and that the similarities this implies extend into the animals' DNA. But while I was idly looking for something to read, I found a blog describing how the recent analysis of the Tiger's DNA reinforces the concept of convergent evolution of wolves and tigers.
As predicted by the hypothesis of convergent evolution between these groups (but not by the idea of common design), Tasmanian Tiger DNA sequence analysis shows that its closest living relatives are the kangaroos and other marsupials, not the placental mammals. (This figure is from Ian Musgrave's blog on the Panda's Thumb.)
Phylogeny based on the sequence cytochrome b. The mid-sized carnivore the Tasmanian Tiger is shown to be more closely related to the vegetarian Kangaroo, and bandicoots and possums, than to its ecological niche and functional equivalents the dog/wolf family. As well, the sequence of the vegetarian Panda is more similar to carnivorous Bears than to other herbivorous animals.
More evidence for common descent (and against 'common design') lies with what Ian Musgrave describes as 'broken genes'. You'll also see them called pseudogenes - copies of genes that have been disabled by mutations but remain in the genome. Because they are non-functional, they can continue to accumulate mutations without this posing any threat to the organism's survival. When scientists look at the genome of animals that we assume on the basis of other evidence (eg fossils, embryology) to share a common ancestor, they find this borne out by the pseudogenes. Organisms that the evidence suggests are closely related turn out to have fewer mutations in their shared psuedogenes. The reverse is true for organisms that are only distantly related - there are more, and different, pseudogene mutations.
Take humans and other primates, for example. Living primates can't manufacture vitamin C - because the necessary gene is disabled - & have to obtain it in their diet. (Fail to do that, & you'll get scurvy.) Analysis of the sequence of this pseudogene shows that humans are most closely related to chimpanzees, which is in agreement with other lines of evidence. (Interestingly, guinea pigs are also unable to manufacture vitamin C, but in their case the disabling mutation is a different, unrelated one.)
Do go and read the original article - Ian's done a very thorough job!