My first campaign with my current group started out as a simple "beer and pretzels" game to introduce a coworker's so to the game, so there was nothing fancy - the PCs met up on the road and decided to adventure together. Only later, when everyone created a backup PC, did I tie the whole group together by having them compete in a "Challenge of Champions" adventure and end up as a cohesive team in an Adventurers Guild.
For my second campaign, I had the PCs all living in the same small kingdom when the king, a former adventurer himself (a retired PC from the previous campaign, as a matter of fact) decide the kingdom needed a dedicated band of adventurers and the PCs were the chosen result. They didn't volunteer - they were "voluntold."
In my current campaign, the PCs all have ties to the Dreamlands - they can each cast one specific 0-level spell (chosen at character creation) and are some of the only people in the word who wake up with perfect memories of their dreams. As such, that made them perfect candidates to be trained by the staff of the Queen of Dreams as dreamwalkers - people who could enter another's dream and interact with it. This was necessary because there was an unexplained "dream plague" going across the continent, where people would be trapped in their dreams while their bodies entered a state of suspended animation, needing neither food nor drink while their minds continued dreaming. That particular plotline just finished up, having taken over half of the 100-adventure campaign.
I've also been a player in three campaigns, two run by my son and one by my co-worker. In the first, the PCs all entered a newly-opened bar and were pressed into service by the king's advisor - they'd be performing tasks the king needed done but needed to have plausible deniability about (kind of like the Suicide Squad, only without us being hardened criminals).
For his next campaign, we all started out as slaves to the drow: four of the five PCs had just been captured, while I ran a lizardfolk PC whose egg had been stolen from the surface and thus slavery was all he knew.
In the current campaign run by my coworker, our PCs all started in Greyhawk City but hired on as security for a caravan heading west for 19 days.
Johnathan