Species names:

Gray squirrel, Sciurus carolinensis
Red squirrel, Tamiasciurus hudsonicus
Fox squirrel, Sciurus niger
Northern flying squirrel, Glaucomys sabrinus
Southern flying squirrel, Glaucomys volans

Size:
Gray:
18–20″ long
Tail half that length
1–1 1/2pounds.
Red:
12″ long
12” tail
About 5 1/2ounces
Fox squirrel:
21″ long, includes 9 1/2″ tail
Nearly 2 pounds.
Northern flying:
10–11″ includes 4 1/2″ tail
3–4 ounces.
Southern flying:
9–10″ includes 3 1/2″ tail
1 1/2–2 1/2 ounces.

Signs of their presence:

The animals themselves.

Sounds: Red squirrels are loudest, with their sometimes birdlike, sometimes scolding, but seemingly endless chatter. Gray and fox squirrels also chatter, and during the mating season, they’ll make a chucking bark as they chase each other. May hear chewing, pattering, scampering, scratching sounds in attic, eaves, and walls from early morning throughout the day—except for flying squirrels, which are nocturnal.

Scat: Oval, smooth, roughly 1/4″ long. The scat of flying squirrels is often found in distinctive piles.

Nests: Gray, fox, and flying squirrels make leaf nests, usually placed in a tree crotch, that are used summer and fall. The flying squirrel’s nest is about 8″ in diameter; those of the gray and fox squirrel are larger.

Evidence of their feeding: Nipped twigs of spruce, hemlock, and pine trees; piles of gnawed hickory nuts and walnuts, or strips of acorn shell, between attic joists or in wall cavities (gray, fox, red, or flying); piles of pine cones, acorns, hickory nuts (red).

Garden and crop damage: They eat flower bulbs and seeds, raid birdfeeders, damage the equipment used for maple syrup collection, eat cherry blossoms and ripe pears, and chew on the bark of fruit trees. They may also strip bark, which they use in their nests.

Building damage: Holes in vents, eaves, soffits, and fascia. Claw marks on siding. Tunnels in insulation. Chewed wires. Damage to stored household goods, either from their chewing, urine, or feces.

Common nuisance situations:

Time of year: Any time of year.

September through February, denning activity. Typically, an attic den could be home to 8–10 squirrels (red or gray squirrels) or dozens of flying squirrels (perhaps up to 50).
From March through May, breeding, as females seek places to raise their young. That’s when you typically find one female and her young in the attic or wall.
They den in attics, walls, sheds, barns, and chimneys, annoying people with their noise and odors. Squirrels usually gain access via overhanging branches, power lines, or by climbing up the siding. They may fall into chimney and furnace flues, thus gaining entrance to the basement or interior of the house.

Their nest materials might block a vent, causing a fire hazard.

They chew and scratch wires (another fire hazard) and also damage attic vents, eaves, screens, bird feeders, siding, insulation, household goods, and the tubing used for maple syrup production.

They run along power lines and sometimes short out transformers.

Squirrels also eat garden, field, and orchard crops; bird seed; and newly planted vegetable seeds.

They’ll strip the bark from trees, especially fruit trees and cedar.

Disease risks: mange, cat scratch disease, typhus, rabies (rarely).
For more information:
http://www.nwco.net/08-AppendixBNuisanceSpecies/8-12-Squirrels.asp