Pillbugs, also called sow bugs or isopods, are actually crustaceans, not insects. I find them all over the place in my yard, but they particularly like my compost pile. This makes sense, because isopods' food of choice is decaying plant matter. Isopods play a key role in any organic garden by breaking down leaves and other plant matter into the soil, enriching it with all that healthy organic content. Occasionally, pillbugs will eat small seedlings or plant roots, but I've never really had much of a problem with that. The U.C. Davis website recommends watering in the morning so your soil dries by night to help control the population. To keep my pillbug population down, I pour my compost on the ground and let the chickens snack on the bugs for a few minutes before spreading it in the garden. (You have to watch the chickens closely, though, or they'll scratch the compost around and fling it all over the yard.)
Verdict: Mostly friend
Telltale signs: Little grey, shell-wearing wandering around the soil surface
How to get rid of them: Manage soil dampness, let your chickens eat them, or, you know, just let them be.

Aphid

I probably hate aphids more than any other garden pest. They are sneaky and small and extremely difficult to eliminate. Plus, it takes forever to wash them off of greens when you're trying to make dinner. I have lost many a broccoli, kale or brussels sprout plant to aphids and their evil sap-sucking. These tiny green or grey bugs latch onto the bottoms of leaves and suck out all their juices. Leaves with infestations turn white or yellow and eventually die. Aphids multiply quickly, so if you notice them on a plant, it's best to get rid of them right away.
Verdict: Foe
Telltale signs: Yellow or white withering leaves, small groups of grey or green bugs on the underside of leaves.
How to get rid of them: Ants "farm" aphids, so one way to keep them from ever appearing is to keep ants out of your garden. You can try sprinkling dioatomaceous earth or boric acid around plants to kill the ants. When aphids appear, try spraying your plants with an organic soap spray. I've had limited success with this method. The best method is to encourage beneficial insects like ladybugs and praying mantis, which both eat aphids. I don't have many ladybugs in my garden, but when they do show up, they really do a great job of gobbling up aphids. I also suggest pull any plants where the aphid infestation gets really bad.

More garden insect resources:
U.C. Davis "How to Manage Pests"
Northwest Coalition for Alternatives to Pesticides