In Genesis 15, Abram was told in a vision:

(1)  After these things the word of the LORD came to Abram in a vision, saying, “Do not be afraid, Abram. I am your shield, your exceedingly great reward.”…
(5)  Then He brought him outside and said, “Look now toward heaven, and count the stars if you are able to number them.” And He said to him, “So shall your descendants be.”  (6)  And he believed in the LORD, and He accounted it to him for righteousness.  (7)  Then He said to him, “I am the LORD, who brought you out of Ur of the Chaldeans, to give you this land to inherit it.”
(8)  And he said, “Lord GOD, how shall I know that I will inherit it?”
(9)  So He said to him, “Bring Me a three-year-old heifer, a three-year-old female goat, a three-year-old ram, a turtledove, and a young pigeon.”  (10)  Then he brought all these to Him and cut them in two, down the middle, and placed each piece opposite the other; but he did not cut the birds in two….
(12)  Now when the sun was going down, a deep sleep fell upon Abram; and behold, horror and great darkness fell upon him….  (17)  And it came to pass, when the sun went down and it was dark, that behold, there appeared a smoking oven and a burning torch that passed between those pieces.
(18)  On the same day the LORD made a covenant with Abram, saying: “To your descendants I have given this land, from the river of Egypt to the great river, the River Euphrates  (19)  the Kenites, the Kenezzites, the Kadmonites,  (20)  the Hittites, the Perizzites, the Rephaim,  (21)  the Amorites, the Canaanites, the Girgashites, and the Jebusites.”

The next time a pigeon is mentioned is after the birth of a child, a woman was to bring a sin offering.

‘When the days of her purification are fulfilled, whether for a son or a daughter, she shall bring to the priest a lamb of the first year as a burnt offering, and a young pigeon or a turtledove as a sin offering, to the door of the tabernacle of meeting. (Leviticus 12:6 NKJV)

In North America we have four pigeons that are in the Order Columbifomes, which contains 300 plus species. This includes pigeons, doves, and turtle-doves plus others. The size of the bird helps distinguish between “doves” and “pigeons”, with the “pigeon” being the largest. Our Pigeons are the:

The Rock Pigeon (previously the Rock Dove), “Male, 12.2–13.4 in (31–34 cm), 6.3–12.5 oz (180–355 g). Plumage generally bluish gray with relatively short tail and long, strong wings.” “The rock pigeon has a rather fast and long step. It is a skillful flyer. Flight velocities of 115 mph (185 kph) have been recorded.”  “Carrier pigeons deserve special mention. Pigeons have been used to send communications since earliest times. In ancient Egypt, Pharaoh Djoser (2600–2550 B.C.) released house pigeons at the borders of his empire to mail the news that enemies were attacking the frontiers. Today’s carrier pigeon was created about 1850 in Belgium by breeding various races. Carrier pigeons can cover up to 621 mi (1,000 km) in a single day, and were trained to live with two lofts 12.4 mi (20 km) apart.” (About.com)

White-crowned Pigeon

White-crowned Pigeon, is 13 in long, has a wingspan of 23 in and weighs about 8 oz. “The adult is dark grey, with green and white bars on the nape, a brilliant white crown to the head, a white iris, and a pale-tipped red bill.” “The ground speed of the White-crowned Pigeon in flight has not been formally documented, but is said to easily outpace a fast motorboat.” (All About Birds)

Band-tailed Pigeon, is 13-16 in and weighs 12.5 oz. and has a yellow bill and feet. “The plumage is gray, somewhat darker above. The head and underparts have a faint pink cast, especially in the adult male; the belly is nearly white.” (Western Field Guide)

Red-billed Pigeon – is 14 in and a large pigeon, that is gray and deep maroon, with a red bill with a pale tip.

“Pigeons and doves are distributed everywhere on Earth, except for the driest areas of the Sahara Desert, Antarctica and its surrounding islands and the high Arctic. They have colonised most of the world’s oceanic islands (with the notable exception of Hawaii), reaching eastern Polynesia and the Chatham Islands in the Pacific, Mauritius, the Seychelles and Reunion in the Indian Ocean, and the Azores in the Atlantic Ocean.

The Band-tailed Pigeon is the largest in North America. The Passenger Pigeon, which has become extinct, at one time had over 4 billion in number. One report mentioned that on a fly-over the pigeons were in a flock, “a mile wide and up to 300 miles long, were so dense that they darkened the sky for hours and days as the flock passed overhead.” (Chipper Wood Bird Observatory)

The family has adapted to most of the habitats available on the planet. The largest number of species are found in tropical forests and woodlands, where they may be arboreal, terrestrial or semi-terrestrial. Various species also inhabit savannas, grasslands, deserts, temperate woodlands and forests, mangrove forests, and even the barren sands and gravels of atolls.” From Wikipedia

“The Common Bronzewing (Phaps chalcoptera) is a species of medium-sized, heavily built pigeon. Native to Australia and one of the country’s most common pigeons, the Common Bronzewing is able to live in almost any habitat, with the possible exception of very barren areas and dense rainforests.” From Wikipedia

Pigeons in a group are called a “loft,” “band,” “dropping”, “passel” or a “school” of pigeons.

Links from WhatBird.com
Red-billed Pigeon
Band-tailed Pigeon or Band-tailed from All About Birds
Rock Pigeon or Rock from All About Birds
White-crowned Pigeon or White-tailed from All About Birds
Here are some of the Pigeons Worldwide: