My favorite insects might be dragonflies and damselflies. We have a few different species that frequent the yard, thanks to our small pond. These two pictures are of male Neon Skimmers (Libellula croceipennis). Notice the interesting place where the one on the right chose to land...!
This dragonfly looks a lot like the Neon Skimmer, but it's a duller red (the females are actually more tan in color) and has different minor striping. It's a Needham's Skimmer (Libellua needhami). One summer we had dozens of them fighting for dominance over our pond. The females would lay their eggs in water droplets they splashed up onto the shoreside vegetation, which was cool to watch.
This is a Roseate Skimmer (Orthemis ferruginea) - the only North American dragonfly to be bright pink.
This is a Common Whitetail (Plathemis lydia). It's a female. The males have the white abdomen that gives the species its common name.
Here is a Black Saddlebags (Tramea lacerta), so named because of the spots at the base of the wing like the bags on either side of a horse's saddle.
A Broad-winged Dragonlet (Erythrodiplax umbrata).
Dragonflies lay their eggs in water. The young hatch and live on the bottom as a larval stage known as a naiad. When they mature, the naiads use a piece of vegetation to climb out of the water, molt for a final time, and emerge as an adult. This is the molted exoskeleton from a dragonfly naiad.
The dragonfly on the left (above) is an Eastern Pondhawk (Erythemis simplicicollis). She had recently emerged from her naiad exoskeleton. The process was difficult, as the crumpled wings and abdomen will indicate. On the right (above) is a male Great Blue Skimmer (Libellula vibrans).
This is a female (left) and male (right) Blue Dasher (Pachydiplax longipennis). Notice that female Blue Dashers are not blue. Most dragonflies have males and females with different coloration.
To the left is a Spot-Winged Glider (Pantella hymenea), identifiable by the dark spots at the base of the hind wings (by the abdomen). I took this photo through the window during a rainstorm. I had hypothesized that the dragonfly might have adopted this posture to minimize the number and effect of raindrop hits, but it turns out that this species often perches this way, regardless of the weather.
Here is an Eastern Amberwing (Perithemus tenera), a very small dragonfly (about the size of a quarter).
These are damselflies. The one on the left is a female Ebony Jewelwing (Calopteryx maculata), and the one on the right is probably some type of American Bluet (Enallagma species). Damselflies are like dragonflies, but smaller. Their wings are attached differently, and are able to fold closed over the insect's back.