The oldest or most ancient insect (bug) known today is called Rhyniognatha hirsti. It was found fossilized in red sandstone in Aberdeen, Scotland.

Anatomical characteristics of the fossil's jaw identify it as a true insect. Although it share features with winged insects, it is impossible to confirm that indeed it could fly since the wings themselves are missing from the fossil. The fossil suggests that insects were among the earliest animals to live on land and that winged flight may have evolved in the Silurian Period, some 438-408 million years ago.
To read more about the discovery check out this website: oldest insect