About three years ago we had a bit of a light-hearted brainstorm about this subject. Most of our thoughts (for some reason) centred around "The Love Boat" as an example campaign. We posited the action taking place onboard the S&S equivalent of a cruise liner, with the PCs taking the parts of the various crew members. We came up with various adventures, ranging from the crew dealing with the complications of the private lives of their passengers, to repelling the attentions of predatory pirates. At the time I produced a small PDF outlining some ideas on how to do Merchant Marine PCs for S&S 1e.
The PDf is still up on Google Drive:
https://drive.google.com/file/d/0B9m0sXWdlPDQNGY3ZjlmZWMtNDAxYi00MzhkLTlkY2EtYWM4ZTAzZTY5ZTRh/edit?usp=sharing, if anyone is interested.
The PDF assumes that there is a Confederation-wide Merchant Marine, as well as smaller companies. However, for rating purposes (read creating PCs), there are standards that have to be met for the PCs to be accredited as traders.
You could also check out the Pirates of Vega thread for my ideas on an equivalent of the Orion trading clans.
With S&S2e, I've been considering updating my ideas on the Merchant Marine, and also been giving some thoughts to merchant-based campaigns.
Obviously, there is the "tramp freighter" campaign beloved of old-school Traveller games. However, in its pure form, I think this is quite unsatisfying. It requires trying to set up an economic system, with the PCs trying to make enough money to keep ahead. If you have the post-scarcity society of Star Trek post-TNG, then this is a bit pointless. It is also not a lot of fun to pilot a spreadsheet.
Fortunately, I'm not a believer in the cashless society, being more an old-school Trek and SFB kinda guy. There is a point to trading in my version of the setting. This allows merchants, but it's probably still very unsatisfying for the majority of gaming groups.
The next stage would be playing the important members of a trading group - a cartel, a family of free traders, or a corporation. If you treat the economic activites as happening "off screen" or in down-time, then you can concentrate on the activities going on that surround the day job. By this, I mean things like opening new trade routes, negotiating contracts, politics and rivalry. This puts the game more on the level of a soap opera - but what the hey! It's about the characters. The level of action would depend on the size of the PC organisation.
The Love Boat option is another possibility. This is similar to a standard S&S campaign, in that the PCs are members of the crew. While they don't have much control over the running of the vessel, they can do a lot of interaction with the NPCs. This is quite a light-hearted option.
I've been considering other possibilities for a non-military scif-fi campaign in my off-moments. For example - what if the PCs were crew of a salvage or repair vessel? The action in that would centre around what the PCs find in the space lanes and how they deal with it. The PCs would not have to be the elite of Star Fleet, and could probably get away with being the opposite. Another example - the PCs are trading scouts, finding new planets and societies to open trade with. This would involve a lot of "first contact" situations.
Just some thoughts.