Where to start...
I've been playing Traveller for years and must've run at least a dozen campaigns of it more or less. They've ranged between fairly hard science war stories to more swashbuckling space opera adventures. I almost always set my campaigns in the Third Imperium at different periods in its history.
I ran one game where the PCs were the crew of an independant scout vessel working for the Imperial Interstellar Scout Serivce to complete a project called The First Survey. For those not familiar with Traveller canon lore, the First Survey was a monumental project undertaken by the Imperium to try and identify and catalog all the planets within its sphere. Many of these were little more then a set of numbers or planet names in the Scout databases and had never really been explored. IMTU, the Scout Service becomes overwhelmed at some point and starts hiring independant vessels to help out, especially those whose captain's are former Scouts. This is wear the PCs come in. Imagine Star Trek in a more hard science universe.
My next campaign was set nearly 600 years later and for all the players knew it was completely unrelated to the first one. This new campaign followed the adventures of a corporation that served to supplement the thinly stretched forces of the Imperium on its distant frontier. The PCs were troubleshooters of a kind, fighting pirates, performing search and rescue missions, negotiating with aliens and many covert operations against enemies of the Imperium (sometimes the Imperial government was their client). There was always some indication that the company had rights and powers it shouldn't really have but the upper-ups (CEO, Vice President, etc.) had some major connections and were owed major favors. The major arching plots and reoccuring villains were a fleet of pirates who were more like an organized crime cartel, a competitor corporation with a hidden aggenda, a search for Ancients arifacts and the political manuverings of the companies friends and rivals. The origin campaign influenced this one in subtle ways...family nanes from the original popped up from time to time and the discovery of an ancients site in the original played a major role in this second one.
Its late now but I'll try to remember some of our other campaigns as soon as I can.
AD