Why Work Together?
I was having problems with party cohesion, so I started a campaign with the rule that all of the characters grew up together on an island. The first adventure was the party saving the island from a curse that turned everyone into statues. (The party were on a ship at the time, away from the island, so they weren't cursed.) By the time the party completed the series of adventures to get the ingredients to remove the curse, they had gained a couple of levels and no longer fit in on the island. They were completely different people. So, they had to band together for further adventuring, because each other was all they had.
Several times, I have gone with the powerful patron hiring the group.
One campaign, one of the PCs was a knight in the king's service. (Very Arthurian.) The rest of the party either served him, his family, or had been hired by the king to help out. (This only works if the players can accept the leader. In this group, it worked.)
In one campaign where I saw absolutely no reason for the party to group up, I had them all hired by the big university to help out with an expedition. Each of the party members was either hired for knowledge or combat ability. Then I started killing off expedition members at the site until the party had to work together to survive. (Unfortunately, the playing style of the players were just too diverse, so the game finally ended.)
Now, I follow a simple rule. Everyone sits down around the table and makes their characters together. You have to tell everyone else the general outline of your character. You can keep your secrets. This avoid problems like one character being all about exploration when another is a politician tied to a specific area, or one character despising and killing on site members of a race that someone else is playing. (I don't mind some tension, but it's no fun when the party has to stop one member from killing the other due to an accident of birth.)
Perhaps it's a little lazy as a DM, because I don't come up with ways to unite the party, but I figure if I went to all the trouble to develop a campaign, the least the players can do is come up with why their character would be a part of it -- and of the group as a whole.