PC motivations usually fall somewhere between "I like money" and "I don't like that guy." In there is the driving force that leads most PCs to risk their lives. Isn't there anything deeper than that going on? These PCs often have very rough origin stories. Most of them lost their parents at a young age and had to practically raise themselves. Let's try to add something to that.
The PC driven campaign requires a different outlook on how missions are given. You aren't going to want that mysterious stranger in the tavern ordering the PCs around for petty amounts of gold and "whatever they find in the dungeon." No, your missions will come straight from the PCs' backstories. They will create their own missions and you will set them up. The goal of this is to have the PCs actively searching for what they seek. Whether they find it through rumors, by accident, or from that mysterious stranger, the point is they find it and not the other way around.
Money and Treasure
This PC seeks money and treasure, and not for greedy reasons. This PC's parents (if they live) owe a debt that they cannot pay and the PC seeks the funds to save his/her parents. This PC may also seek to one day open up a shop in a big city and saves for that day. Perhaps, the PC seeks only to contribute all of the money and treasure he/she finds to his/her temple or church.
This PC is looking for a series of shrines or some other artifact. Maybe, the church sent this PC out to pray at shrines across the country, or maybe they sent this PC to find a special artifact for the temple. Maybe as a right of passage, this PC must single-handedly defeat a giant and bring it's head back to his/her tribe.
Out for Blood
This PC has an enemy that he/she seeks to vanquish. This enemy could be something like "all goblins" or "the man who murdered my parents." It could also be more vague like "all evil." Whatever it is, this PC is actively hunting it.
Glory and Honor
This PC seeks glory and honor for reasons of pride or to honor his/her parents or church or tribe. This PC will take on difficult, high profile jobs that will put him/her in the spotlight. This PC may already be famous in some places.
Some of these could take charge of a campaign if you are not careful. Remember that every PC will have motivations and will want to fulfill his/her goals, so don't let the game focus on just one.
At least two things can come from this type of campaign. The in and out game where each PC leaves the group after accomplishing his/her goals and then the player brings in another PC to replace the one who left. Or, the bonded campaign where, having completed his/her task, the PCs stick together until everyone has completed his/her quest.
Feel free to change, use, and abuse this idea in any way you like.