I've done a few campaign intros over the years....
My first was an old fashion, "You're sitting in a tavern when...." That campaign (a Planescape one) started almost five years ago and is still going after only a couple of breaks. It's also my best one (campaign, not intro) by far.
I started one with a little prologue in which a very old man sits down with his many great grand children and begins to tell them a story from when he was much younger. The beginning of his story turned into the beginning of the adventure. My intent was, by the end of a long campaign, to have the old man finish his story (marking the end of the last adventure and the campaign), revealing that the man was one of the characters. But alas, we had a total party kill in our third adventure (to the grimlocks in the abandoned warehouse in "The Speaker in Dreams.")
I tried to start one in which the characters had already been adventuring with each other for a few weeks by asking the players to talk about their characters. I guess my players were unprepared for this and couldn't think of much to say, so it became kind of awkward. This was probably my worst campaign intro.
I started another one where the characters were to have been adventuring with each other for a few years by having them attend dinner with the mentor of the party wizard. The mentor had his old adventuring buddies over. I thought it was interesting to see a new adventuring party interact with an old, retired adventuring party.
Finally, I started another one (another Planescape one) in which each character, individually, was attacked and captured by a pack of ghouls lead by a Keeper (bald, pale-skinned guys who wear goggles), wake up briefly to being examined by strange beings, then wake up again (sans gear and clothing) together in prison cells, each with a tattoo on one of their hands. They needed to cooperate in order to escape (it was funny, a half-dozen, naked, level-one adventurers standing on each other's shoulders to reach the cell’s exit in the ceiling, far above. Too bad the guy at the bottom was a tiefling and had hooves instead of feet--he slipped on the first try....).
Later,
Atavar
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"Ahhh, ah ah ah....bitter dregs"
Mr. Spock