Another approach is to have PCs who do not know each other at all, and give each of them an entirely different reason to be in the same place at the same time, throwing their lot in together almost accidentially because of circumstances.

The campaign begins with a grand ball. One of the PCs is a minor lackey/guard in the hosting mansion (1st level fighter). Another is attending as a punishment for misbehavior as a servant (1st level wizard, apprentice to a more powerful wizard). A third has slipped in hoping to make a quick buck (1st level Rogue), while the fourth is actually invited (1st level Bard).

During the grand ball, evil mastermind that the PCs won't actually face until they're 12th level or so shows up, blows a lot of people up, steals the duke's daughter or somesuch, and disappears with her.

Each has their own reason to pursue BBEG. Fighter = make up for failing to protect, get back for the slaughtered fellow guards. Wizard = revenge for killing master. Rogue = Serious $$ for rescue reward. Bard = secretly in love with said duke's daughter. They work together just because there is safety in numbers and each brings useful skills to the table.

Yes, there's a lot of cliche in this too...but it's just a quick off-the-top example. The point is that the group doesn't have to all have the same reason to pursue the goal, and more interesting RP can often result if they do differ, or even have opposed reasons.