Potoos!

Well, and a couple of guira cuckoos.

Potoos, the crazy birds of Internet fame, are weird critters. They spend their days sitting on stumps, disguised as pieces of rotting wood, except for baby potoos, who are white and apparently imitate growths of fungus. They even lay their eggs directly on the stump, not bothering with anything as mainstream as a nest. At night, they open their insanely large eyes and start catching flying insects and little birds from the air, like monstrous flycatchers.

There are seven known species of potoo, all living in tropical New World. They all look very much alike, to the point that some pairs of species simply cannot be separated based on appearance, and there probably are more cryptic ones to be found. Despite this, potoo species seem to be very, very old: these apparently identical birds differ genetically as much as whole genera or even families in other birds. Which basically means they have been sitting on stumps, not changing a bit, for millions of years.