While players can work as a team and design their characters that way, they have almost total control over the creation of their PCs as far as personality, trade, and background is concerned. In some cases, GMs may ask the players to create whatever they like and then bring the PCs together in the first game. This gives the players free rein as to how they want their PCs to be, but can create a problem as to how these PCs come together.
There's nothing more decisive than the Queen/Emperor/Ruling Faction pointing a long bony finger at the PCs and saying, for example, 'I command you to walk to the Ring of Fire and defeat this evil!' Already the PCs have been given a good reason as to why they should adventure together – they've been given their orders!
Of course, you have to ask the question, in some respects, as to why a certain PC should agree to such a thing. Let's take the example group:
The group has been given their orders by their ruler and will do all they can to win through, even though they are a mismatched group of PCs from very different backgrounds. It makes for excellent role-playing. It's also an excellent way to bring the PCs together and keep them together.
Even though PCs may come from different backgrounds, it is still possible they might be friends. Although there might be a class system in effect in your game world, it is still possible that certain people might go against the grain and mix with whomever they wish and not with their social class or kind.
The noble in our example group might be a man who likes to 'slum it', a PC of great esteem who dresses down and walks the lower streets of the city, mixing with what he would usually see as undesirables. In this group he finds new friends: a mercenary, a nurse from the local physician's guild, and (unknown to him) a horse thief.
Alternatively, the mercenary could have gotten a job as a guard at the noble's castle, the nurse could work as a surgeon there, and the horse thief could 'work' in the stables. As the three mix on a daily basis they get to know each other.
So, when disaster does strike or one or more of the PCs are drawn into a quest, the others are motivated or bound by loyalty to help. Something might happen to them all when the whole group is together and this gives them impetus, as a group, to set out on their quest.
Let's say the PCs are all together in the Great Hall when an attempt is made on the life of the Queen. They might become the only witnesses who saw the assassin so they are sent as a group to track down the enemy.
The PCs might come together because they are all after the same thing but for a different reason. They may be searching for a murderer, an enemy who has affected their lives in some way, or an item that has the ability to solve their particular problem. Each PC has their own agenda and reason as to why they are on the quest and they come together to benefit each other.
This might be tricky. Of course, if they are all after the same thing, then when they do finally achieve it they will all have their own claim to it, especially if it involves an NPC. Unlike an object, which may be shared between the PCs, they will all want their own revenge or justice against the enemy – and there is only one of them to go around. This could make for a fantastically charged role-playing opportunity at the end of a long campaign, but it may be best to split enemies up and have them all part of a greater threat so that each PC has their own closure at the end of the game.
So, for example, the mercenary may be after a man who killed his father, the nurse might be after the same man because he stole her family heirloom, a Pendant of Healing, the noble might be after him to stop him from threatening his borders, the horse thief might be after him because he has been hired to. Each PC has a different reason to go on the quest but, ultimately, they are after the same thing.
A simpler way to get the PCs together is to have them all go on a quest for exactly the same reason. They can then work together and share any rewards reaped at the end.
This can be anything from 'stop the bad guy' to 'find the treasure'. They all believe in the same thing and that shared belief brings them together. It could be a loyalty to a religion or figure of importance, or they know that there is a lot of gold to be made and it serves them all to work together and split the booty. A shared goal, especially when each player is aware that there is more chance of success in greater numbers, is a fine reason for them all to come together.
For example, the PCs hear in a tavern that there is gold in them thar hills and they all share a common need for more gold. The mercenary is up for a quest because he knows his sword may be needed and wishes to make sure his skills are justifiably rewarded. The nurse might want money for her hospice and joins the quest to help finance it. The noble might join to increase the wealth of his family's and his personal coffers, and the horse thief might join because, hey – it's money, and it sure beats stealing horses.
Wouldn't you believe it? The PCs are all in the same place when bang! something terrible occurs and they are all forced to work together to solve the problem. Don't you just hate it when that happens?
Starting a game this way gives the PCs something to focus on straight away and also provides an excellent reason as to why they are required to work together.
Each player has their own reasons and agenda, that much is sure, but when events transpire against them and they must rely on those around them then they will still have their illusion of free will but know they have to team up to survive or overcome the immediate problem. Once that problem is solved or avoided, then the PCs with their knowledge of the threat or problem can continue to work together.
For example, they could be arrested together as scapegoats on a drummed-up charge, or be in the same village when it is attacked, or be in the same castle when it is besieged.
Or, let's say the PCs are all journeying across an ocean on a huge passenger ship when suddenly they're attacked by the forward ships of an invasion fleet. The PCs, close together in a confined area, had to fight side-by-side to defeat the threat. The mercenary will fight because that is what he does. The nurse will fight to defend the wounded. The noble will fight because it might be his ship the raiders are attacking, and the horse thief might fight because where there are bodies, there's looting. Saving each other's lives or aiding in battle will introduce the PCs to one another and strengthen their new relationship.
Although complete player control over the creation of a PC might be great for the dynamics of the character, it may present some problems the GM may have to overcome.
It is a game of fun and adventure, after all, unless the group has something else in mind. If the player is going to refuse every road, avoid every danger, and otherwise do the opposite of what is required to complete the quest, then there's not much point in that PC being present.