A couple of years back, when the majority of the ICON game traffic was held on an emailing list, someone suggested the Junior Explorers of the Federation A Federation based 'Boy Scout' movement.
Its one of my favourite pieces that I have ever seen, so original and yet so obvious that nobody thought of it sooner...
So in a similar vein. I would like to suggest yet another Federation organisation outside of Starfleet, again based on a real organisation in service today;
The Federation Peace Corps.
A Civilian organisation that often works closely with Starfleet, but where Starfleet survey and explore, and where colonists build, the Peace Corps help. Like Starfleet they have the Prime Directive to stop them developing societies that are too primitive, or making contact with species that are simply not ready yet. However there are hundreds of worlds in the Federation, and even more known but un-affiliated, and some need help.
The Peace Corps are an organisation of specialists, from Farmers, Construction Specialists and Doctors, who travel to planets in need of help, and try to improve the life of those in need. Often seen on Struggling Colony worlds or after great Disasters, or even helping rebuild worlds after devastating wars... fro example the Peace Corps was heavily active on Bajor when Starfleet took over DS9, and many of its specialists have been assigned to Cardassia following the Dominion War.
This is just an idea right now, but I will try and get a template or two up later if anyone is interested...
Anyone that wants to see where I might be going with this, or even join in with templates and tours should see;
http://www.peacecorps.gov/indexnf.cfm