Are there any species with non-extinct evolutionary ancestors?

None of the existing primates are our evolutionary ancestors.

The Kakapo, a flightless parrot from New Zealand.
http://www.kakapo.net/en/

Are there any species with non-extinct evolutionary ancestors? That isn't a question, everything alive has evolutionary ancestors all around it, in the large view.

If what you really mean is evolutionary predecessor species, again that is kind of a relative.
There's another living "fossil" in NZ: the Tuatara. But there aren't supposed to be any other species in the same genus (it's a dead-end). But it must have had a common ancestor with, say, crocodilians, or land tortoises, maybe?

Genetics and the newer ways of classifying and comparing the whole show, shows that there must have been a common ancestor for us and the other apes. "Us" is just a single surviving species from a much bigger family of anthropoid apes, that co-existed for millions of years.

Yeah. Termites. Cockroaches are their ancestors.

Wasps. Ants are their ancestors.

Dogs. Wolves are their ancestors.

Cows had a living ancestor until recently (aurochs).