The Avengers

1960s
The evil god Loki (guy on the left) was trapped on an island in
Asgard (home of the Norse gods) by Thor (guy on the right). So, he wanted revenge. He made the Hulk (left to Thor) attack a railroad track, by making him think there was TNT on it. Rick Jones (the Hulk's sidekick) tried to call the Fantastic 4, but Loki sent the transmission to Thor, but Iron Man (in gold metal suit), Ant-Man (on the ants) and Ant-Man's girlfriend The Wasp (left to Ant-Man) also got the transmission. While they fought the Hulk, Thor figured out Loki was behind this and beat him up. The 5 heroes decided to be a team, the "Avengers"! However, the team's ranks began to change. In the second issue, Ant-Man become Giant-Man and the Hulk left the team, because when Space Phantom took his form the rest of the team quickly turned on him, making him mad. The team decided to try to find and contain the Hulk, leading them to battle with the Sub-Mariner. In issue 4, Captain America (who would later become the leader) joined. The teamed battle Baron Zemo (a foe of Captain America) and his version of Masters of Evil; Kang the Conqueror; Wonder Man (unconnected to Wonder Woman); and Count Nefaria. The next important event in the team history every member (but Captain America) quited the team. So, now three former villains (Scarlet Witch, Quicksilver and Hawkeye) joined. Despite a lack of "raw of power", they managed to defeat Swordsman, Power Man I and Doctor Doom. Henry Pym (Ant-Man) and Wasp decided to rejoin the team. Hercules joined the team and so did Black Widow and Black Knight (although they didn't become "official" members, until years later). Thanks to Roy Thomas, Black Panther and the second Vision joined the team. Roy made it so Iron Man funded the team and Edwin Jarvis was there butler. Their new base was super-hi-tech.
1970s
The team battled the Squadron Sinister and was caught in the middle of the Kree-Skrull War. A group of Skrull (shapeshifing several of the heroes) managed to disband the team, but the true founding members (except Wasp) reformed the team thanks to Jarvis. Scarlet Witch fell in love with the Vision (who felt unworthy being a robot). Mantis joined the team with the reformed Swordsman. In a complex series of events, it's reveal Mantis is really Celestial Madonna and her future child will save the universe and the Vision is made out of the "dead" remains of the Human Torch I (not the FF member). Jim Shooter created several storylines, in which Beast of the X-Men, Ms. Marvel, Wonder Man (brought back to life) and Falcon. Henry Peter Gyrich (a member of United States National Security Council) was introduced. He forced the team to only have seven members max. Hawkeye got kick out so Falcon could have his slot (because he was African American), but Falcon decided to quit, because he perceived this as tokenism.
1980s
Henry Pym had a mental breakdown. Egghead impersonated him and got Pym was jailed. However, Pym managed to prove his innocence by defeating the newest version of the Masters of Evil. But, this seriously damaged his relationship with Wasp. He quit from being a superhero (although he would return). In the 1980's, many notable storylines such as "Ultimate Vision" (where Vision tried to take over all the world's computer and tried cause world peace) and "War on Olympus" (where Zeus blamed the Avengers for Heracles getting hurt). New members of the team included the second Marvel comic Captain Marvel, She-Hulk, Tigra, Namor, Starfox and Mockingbird (Henry joined the West Coast Avengers [formed in the "Ultimate Vision" storyline]). They met a new foe, Nebula, who falsely claim to be Thanos' granddaughter. The Avengers moved into the Hydrobase, when their mansion was damaged. The Hydrobase was destroyed during "Acts of Vengeance".
1990s
The two Avenger teams merged into one (but with two bases). Scarlet Witch goes insane upon discovering her children were merely illusions and the "death" of the Vision (he was taken apart by government agents), but her insanity is cured. It was revealed SW could potentially warp reality (which is important for the "Chaos" & "Avengers Disassembled" storylines). The Avengers were in the middle of the "Acts of Vengeance" crossover (where the villains decided to target different heroes than they usually do). But, the villains' plan to destroy the Avengers failed. The team became two teams again. The team was revamped so it members were Black Knight, Sersi, Crystal, Quicksilver, Hercules and the Vision. Around this time, they start to face even more murderous foes, causing them to question the "no killing" rule. During "Operation: Galactic Storm", they Avengers decided to split up, when Iron execute the Supreme Intelligence, despite the wishes of Captain America. The West Coast Avengers disbanded. The team was sucked into alternate reality in "Heroes Reborn", but out.
2000s
The team got international authority. In "Avengers Disassembled", the Scarlet Witch went insane and kill many of team's members and the remaining members quit the team. To respond to mass prison break, Captain America and Iron Man formed the New Avengers. Luke Cage, Spider-Man, and Spider-Woman I, Ronin, the Sentry and Wolverine joined the team. During the Civil War, Captain America formed a splinter group to rebel againist the Superhuman Registration Act. But, Iron Man's group kept the name of the "New Avengers". After the Civil War, the members of the team are Ronin (Hawkeye), Echo, Spider-Man, Spider-Woman, Wolverine, Iron Fist and Doctor Strange. The team battled the ninja-group the Hand and a villain called the Hood. The Avengers (again) were caught in the middle of a big crossover this time the Secret Invasion. After Iron Fist and Echo leave, Ms. Marvel, Mockingbird and Captain America II joined the New Avengers. Iron Man formed the "Mighty Avengers" (in response to the Civil War) with Ares, the Black Widow, Iron Man, the Sentry, the Wasp, Wonder Man and the leader Ms. Marvel (Carol Danvers). All the team, but Ares and Sentry (and Wasp, who died), left when Norman Osborn (the Green Goblin) took over. The team began to work for the Global Reaction Agency for Mysterious Paranormal Activity (GRAMPA). Hercules, Amadeus Cho, Stature, the Vision, Jocasta, U.S. Agent, Quicksilver and Hank Pym joined the team. Iron and the Hulk briefly helped the team. Norman took over Avengers (now funded by HAMMER, which he owns), whose members are Ares, Sentry, Marvel Boy Draken; and Moonstone, Bullseye, and Venom (posing as Ms. Marvel, Hawkeye, and Spider-Man).
2010s
All the Avenger comic titles were replaced by a new Avenger series simply called Avengers. The members (in issue 1) are revealed to be Thor, Hawkeye, Spider-Man, Wolverine, Captain America, Spider-Woman, Iron Man, Steve Rogers (Captain America I), and team leader Maria Hill. Although, they mention an unnamed hero was missing. Noh-Varr later joined the team.
References:
The Incredible Hulk Ultimate Guide
http://en.wikipedia.org/wiki/Avengers_(comics)
http://www.coverbrowser.com/image/avengers/1-1.jpg
Marvel Chronicles