How long ago did the dinosaurs go extinct?

Non-avian dinosaurs died out about 66 million years ago after the Chicxulub asteroid impact. Our species is roughly 300,000 years old, so the extinction is about 220 times further back than the origin of Homo sapiens. Birds descend from theropod dinosaurs, so dinosaurs in the strict sense are still here; the earliest known bird-like dinosaurs are about 150 million years old.

Source: Alvarez et al. (1980), Science; Renne et al. (2013), Science