The campaign I am currently DMing had the players crash land on this proto-world long thought lost by the gods and other beings of the greater multiverse, and deciding to venture out from the small off world settlement they were recovering in to explore the greater world, deciding to do it together because several heads are better then one.
A standard beginning for my group has always been that we have been individually invited by a third party to do a job together, and each member was chosen because of their skills, or reputation, or some other reason that could prove important to the client. Sometimes one of the players acts as the liaison for the mission, other times the DM has an NPC for us to meet for the mission. Sometime the job goes well and the group, seeing the potential for more jobs/money/power, continues to work together to fulfill future contracts. Other times things go wrong and the party must stick together in order to protect our own hides from the slighted parties, or to get revenge on a backstabbing patron.
We have also done the typical origin of all of us happening to enter a town where something goes horribly wrong and our characters end up forming a makeshift team to try and fix said problem. One time it was a town getting attacked and we all jumped in to help defend it, another time a strange disease causes the town to be put under lockdown and our characters try to find the cause or a cure in order to help save people/get us out of the lockdown so we can leave.