(or "Change Is The New Status Quo")
When the Avengers started, it was as one of those ideas so simple that it's practically automatic. If you have X number of stars of X number of comic books that each sell Y copies, you put them all together in one comic and get X times Y sales. Sound business sense, from the Justice Society to the Justice League, and the Avengers didn't look to be any exception. The Hulk, Ant-Man, the Wasp, Thor and Iron Man all teamed up together to fight crime out of a big mansion in New York City, and Stan Lee and Jack Kirby said It Was Good.
But Marvel, in the heady days of the early 1960s, was never afraid to experiment with the storytelling engine of their comics. Unlike DC, Marvel wasn't working with a stable of established characters that needed "protecting". By issue #4, the Hulk had already been ditched in favor of Captain America, firmly establishing the Avengers as a series about a specific type of superhero. The anti-social, amoral Hulk simply couldn't cut it with Earth's Mightiest Heroes, no matter how powerful he was. It set a precedent, but not one completely out of place in team comics--new members joined the Justice League from time to time, after all. Team line-ups were bound to shift a little.
Then along came issue #16, and the Avengers became well and truly established as a comic. Paradoxically, they made their mark by having the entire rest of the founding members of the team quit, all at once. The team now consisted of Cap, Quicksilver, the Scarlet Witch, and Hawkeye...three barely-reformed super-villains and the new guy. (Which just goes to show, as Craig Shutt pointed out, that you should never go to the bathroom during an Avengers team meeting.)
This radical change, so early in the series, really paved the way for the Avengers to become a team book unlike any other. Because the Avengers no longer meant any particular character, or even group of characters (although you do see a lot of the same faces over the years, and some fans will insist it's not a "real" Avengers series without Cap, Thor, and/or Iron Man.) The Avengers suddenly became about the sort of person who would be an Avenger. It became a series about the ethos that would apply to being (I'll say it again) Earth's Mightiest Heroes, and about living up to that ethos. Every character that joins the Avengers feels like they're suddenly playing in a different league, from Quasar to Justice, and "card-carrying Avenger" became, in the Marvel Universe, the cachet for "true hero". That's the engine of the Avengers, and it's what sustains it no matter what the line-up is, no matter who the writer or artist is. In theory, it's the best the Marvel Universe has to offer, fighting its biggest threats...or, at the very least, finding out if they really are the best the Marvel Universe has to offer.
And while I hesitate to end with a simple "it's not as good as it was" statement, this is why neither one of the two Avengers titles currently on the market work as Avengers titles. They might be perfectly good pieces of writing, but Brian Michael Bendis is not writing Avengers comics, no matter what the titles say, because the comics are not about people trying to live up to the standards of the Avengers charter. They're simply random assemblages of super-heroes, no different than any team book on the market. In short, they don't use the Avengers storytelling engine. They simply appropriate its trappings.