I have noticed that many people here talk about their groups' origins and activities. The "how we stole our ship" story is very common, and many seem to be in campaigns where the central background activities of the group is illegal trade (smuggling). There's nothing wrong with this -my own group did this too - but do any of the other options get covered?
It seems like each Career could form the basis for at least one type of campaign. Since Smuggler gets talked about so often, I'm going to skip it.
Bounty Hunter: The group consists of one or more bounty hunters along with specialists that they've partnered with in a life of hunting down the bad guys. Yep, that's right, in this game the PCs are on the right side of the law (mostly). Sure, they may be shady, but they're hunting down even worse bastards for those that can pay. The Empire considers you an independent law enforcement team, but only if you stay clear of taking on illegal bounties. Maybe the PCs can stay clean...
Colonist: The group consists of a group of troubleshooters working for the cause of some legitimate institution. A local government, a university, a noble house, or something similar. Once again, the PCs are legal at the start though they may be tempted to do illegal things. An example of this type of game might be a philanthropist noble and his retinue out wandering the galaxy on his yacht.
Explorer: This one is covered pretty well in Enter the Unknown, but briefly such things as being the crew of a Scout Corps vessel or of being part of an archeological expedition searching sectors for mysteries from the past are ways to play a non-criminal group.
Hired Gun: Here the idea that stands out to me is of playing a legitimate mercenary (private security) force. Because PC groups tend to be small, going for something like high-end bodyguarding (think secret service for hire) could work and would be on the 'right side' of legal. I'm sure that Dangerous Covenants will offer more here.
Technician: Usually support to other roles, a campaign catered on this could easily have the group operating a salvage ship, or something equivalent to a space tow truck. The role of wandering repairmen can fit in here too. These are all legal activities that can be high risk, high reward at times (like actual gameplay) but has low risk, low reward background activity to fill in downtime.
So those are a few of my ideas. I'm thinking of basing my next game on the bounty hunter idea I mention above. Has anyone else opted for a game that isn't criminal-based (particularly smuggling)?