The praying mantis would always startle me when I first saw it in the garden. They can rip the head off an insect faster that you can watch it. Good guys in the garden. The farmers use them as well as ladybugs to control bad bugs.
Owlflies, only distantly related to the true flies, and even more distant from the dragonflies and damselflies. They are diurnal or crepuscular predators of other flying insects, and are typically 5 cm in) long.