Bees
Ladybugs
Like spiders, ladybugs eat other bugs and help to keep the whole ecosystem in balance, especially in your garden. Adults and larvae eat super small pests, such as aphids, which destroy leaves and plants if the get overly abundant.
Praying Mantis
Though closely related to cockroaches and termites, praying mantises are not worth calling the exterminator over. In fact, you should encourage them to live. Their abilities make them excellent predators and their eating habits make them a natural pesticide. If one gets in your house, catch it in a bowl or jar and let it go outside.
Daddy Long Legs
Daddy long legs, while spider-like, are not technically spiders. But like common household spiders, you should leave these guys alone if you spot them in your house. They aren't poisonous to humans and basically couldn't even really bite us (their mouths are too small). They prefer eating fruit and other insects, which they'll happily catch and rid your home of.
Earwig Pincher Bugs
Earwigs seem like they should be dangerous. They're certainly gross to look at, what with that enormous pincer. But don't sweat them, just leave them alone. They use their mighty looking pincers to defend themselves, not harm their good human hosts. And like good guests, they clean up after themselves and others, eating dead insects and decomposing plants in your garden.
Stinkbugs
Stinkbugs, the scourge of church basements and old houses! If you try to squish them or even go after them with bug spray, they'll release a foul odor as their defense mechanism and then you've got squished bugs AND a weird smell to contend with. In the fall, they come in from outdoors to find a warmer place. So, make sure you've got things sealed up and then you won't have to worry about getting rid of them.
Green Lacewings
Green lacewings are also equipped with a stink defense mechanism. But since they cause no harm to you or your garden, they too are best left unmolested. In fact, some people do what they can to keep them in their gardens, because their larvae have a huge appetite for aphids, spider mites, thrips, leafhoppers, white flies and even some small caterpillars, among other actual pests.