Here are the main bird beak, or bill, types:
Short, thick, curved, pointed beaks of hawks, falcons, and owls, adapted for ripping flesh. The beak of a nestling Barred Owl, Strix varia, is shown at the right.
Long, very slender, sharp-pointed beaks, such as shown at the left on a Ruby-throated Hummingbird, Archilochus colubris, in winter plumage, are adapted for inserting into narrow-throated blossoms, to feed on nectar.
Short, wide beaks, sometimes with hooked tips, like that of the Vermilion Flycatcher, Pyrocephalus obscurus, shown at the right, are 
good for catching and holding flying insects. The picture by Dan Sudia at the left is that of a Lesser Nighthawk, Chordeiles acutipennis. Notice the bumps inside the wide, short-beaked mouth. The bumps are slightly pointed and directed backwards in such a way that they help the bird hold onto its food, and keep the food moving toward the stomach. Many bird mouths are equipped with similar protuberances.
Short, slender, sharp beaks adapted for probing into tight places such as bark fissures on tree trunks where small insects, spiders, and other creatures might be wedged; found among warblers, vireos, kinglets, gnatcatchers, and others. The Tufted Titmouse, Baeolophus bicolor, in the picture is using the beak as a chisel to peck through the shell of a small seed.
Broad, flattish, round-tipped beaks of most ducks and geese -- like that of the domesticated Muscovy Duck, Cairina moschata, at the right -- are equipped with tiny, comb-like structures called lamellae along the beak's outer edge. In aquatic environments, the constantly opening and closing beak coordinated with the tongue causes water to rush in and out of the mouth. When passing from the mouth through the lamellae along the beak's sides, small animals, insects and plants from the water and mud are filtered out and gobbled down.
Fairly long, thick, chisel-like beaks adapted for drilling wood and chipping away tree bark, as shown on the female Golden-fronted Woodpecker, Melanerpes aurifrons, at the left.
Short, stubby, but powerful beaks adapted for grinding small seeds, found among sparrows, finches, juncos, and others, such as the Evening Grosbeak shown at the right.
Nestling beaks often are yellow-rimmed like those shown of the American Robin, Turdus migratorius, at the left. In that picture the top bird is the mother but the lower two, with especially broad, gaping mouths, are nestlings. The nestling beaks' yellow rims make easier targets for the overworked adults arriving with food. The birds in the picture aren't begging for food, though, but rather are very hot on a mid-summer day, encouraging cooling evaporation to take place in their moist mouths and throats.
Specialized beaks often show surprising adaptations. For example, at the right the White Pelican, Pelecanus erythrorhynchos, often is seen crashing into the sea and coming up with a fish in its beak. It may flip the fish in the air and catch it again, with a more secure hold, then swallow it whole. As the fish goes down you might see the beak's bottom part grow somewhat baggy. You've seen in cartoons how pelicans have incredibly big pouches in which they can place their suitcases. In real life the pouches aren't as big, but they certainly can expand to hold a big fish. In the picture, the top of the beak bears a fin-like, temporary "nuptial tubercle," which occurs on males during the breeding season. Later, the tubercle will disintegrate. Tubercles are thought to contribute during the mating display.
When the Roseate Spoonbill, Ajaia ajaja, shown at the left, feeds in shallow water, the paddle-like beak tip is dipped deep into the water, to right atop the mud, and -- with the mandibles slightly held apart -- constantly swung back and forth in a sideways motion, as the bird slowly walks forward. When the bird feels something like a shrimp in the water passing through the open bill, the beak is clapped shut, pulled from the water, and the prey is swallowed.
The beak of the Keel-billed Toucan, Ramphastos sulfuratus, is used to reach fruit on branches too small to support the bird's weight, and the bill's saw-toothed margins help peel fruit. You'd guess that the beak's bright colors attract potential mates during courtship, but the bills of male and female have similar markings. The spectacular bill might intimidate other birds, allowing the toucan to plunder their nests, for toucans supplement their diet with eggs and nestlings, as well as insects, small lizards, etc. Maybe the colors and patterns also help camouflage the bird, helping it escape larger predators. In the end, certain parts of Nature just remain beyond the realm of explanation.