In a cyberpunk game we played you had to roll for every year after 16. odds was good year even bad. Then you rolled on the good or bad table. On the bad table it went from something like you were in a minor accident and now have a visible scar at the top of the table to awful stuff at the bottom! i.e. A sibling or parent dies. Then we filled in gaps to create personal enemies, asperations or detailed character history.
This is a bit different, more elegant perhaps, than the Midian DFRPG method. There's a whole chapter of backgrounds (mix of random and choice) that can offer hooks for characters. Players discussing their characters sometimes find commonality in their backgrounds, perhaps indicating a shared experience. In one of the current games, all of the pc's (save one, and he's the most sociopathic) have an as yet undescribed event in their pasts. The running joke is that the thing that brought them all together is 'that terrible thing you did'.
Belonging to the same organisation can bring the pc's together. This is rather a default assumption in Midian, that all of the group will belong to the same guild. An organisation differs from an employer, as there is a reason you are all there besides getting paid. The organisation could be as close and personal as belonging to the same church, or as loose-knit as trolling the same forum.
Another idea, to borrow from the pilot of Caprica, is that all of the pc's are witnesses to the same tragedy. A variation on this is that they are all survivors instead: they were rescued from the rubble, relatives were killed, etc.
Love these ideas, gents! I will add 'guild' or 'syndicate' into the mix too. They could also be together because of a shared belief system. Also, I like the idea of being witness to the same tragedy - more generic than the 'refugees' idea.
MrE - as much as I like random rolling (Icar is mostly random rolls), I think background is too important to the GM for plot traction to take by chance. When sandbox gaming, the background needs to be deliberate.
and then there are some of the existing psychotheatrics like criminal/enforcer parents or criminal conections or explaing some of the results like say the bionic rejection (borged by an amature) or unknown past!