Sometimes we're lucky enough to observe birds close at hand---around a feeder, for example---in which case identification is relatively easy, as long as you've got a good field guide. Most of the time, however, the birds we see around us are fleeting shapes and silhouettes, rocketing through brush or flashing by on high. Some general familiarity with the basic shapes of bird wings goes a long way in improving identifications---and getting a little deeper sense of avian morphology. Much of this information was adapted from the textbook Ornithology (1995) by Frank B. Gill (see References).
Slender, Unslotted, Pointed
The speed kings of the avian world usually have wings that look like slim, crooked blades: narrow, without slots, and pointed. The peregrine falcon, a famed bird-hunter with such scythe wings, can propel itself in speeds in excess of 200 miles per hour in fantastic stoops.
Short and Rounded
Typically, birds with rather stubby wings are quick and highly maneuverable in flight. Such a form allows passerine birds to shoot through thick vegetation, forest hawks to pursue agile prey, and highly-terrestrial species like grouse or quail to swiftly take off under threat.
Heavy, Broad, and Slotted
Big soaring raptors like eagles, hawks, and vultures have long, broad wings with pronounced "fingers" at their ends---slots that reduce drag and enhance lift. While these birds are powerful flappers (even large hawks can "hover" in the face of a stiff wind), they typically reduce energy expenditure by expertly riding air currents, such as thermals (rising columns of heated air) and updrafts created by ridges. Instead of flapping to create forward thrust, for example, a turkey vulture can counteract drag by spiraling up a thermal, then dropping to the foot of another (Gill 1995).
Long and Slender
These wings are employed by pelagic seabirds like albatross for long-distance gliding, and by slow-flapping and soaring birds like nighthawks and swallows. This shape engenders a high wing loading---for example, Gill (1995) notes that, in the heavy-bodied and slim-winged albatrosses, each square centimeter of wing area supports about 1.7 grams of mass.