Arugula is not a subtle plant. Its unmistakable flavor, bitterness, and spicy kick generally make people love it or hate it. When it is tiny--the baby arugula we sell in bags--has a delicate, aromatic flavor; big, bunched arugula is intense and dramatic. Often, our arugula has tiny round holes in the leaves. These are from flea beetles, who are among arugula's biggest fans; you won't find any of them in your greens, since they jump off when harvesters approach. (Summer arugula without holes has probably been grown under row-covers or sprayed with insecticides--ask your farmer!)
Arugula is great added to a salad of mixed greens. The peppery compounds in it are volatile, so if you chop it, it will be tamer. Vinaigrette dressings also mellow its spiciness. In our house, arugula is often eaten on its own, with olive oil, salt, and pepper; chopped onion and grated cheese are good on that too.
You can cook arugula; it still tastes like arugula, and is still a bitter green, but loses its heat entirely. Use it instead of mustard or spinach; it cooks very quickly. Substitute it for basil in pesto (see the basil recipes) for a non-spicy but very arugula-flavored treat--it stays green, too.