Often when you picked up a mission from one of the terminals, there would be a logical reason for the NPC who wrote the "help wanted" message hiring you. A farmer might want you to kill a swoop gang that was terrorizing him, or a cowardly Trandoshan whose reputation depended on him killing an animal he was too scared to face might want you to do the job for him and then let him take the credit. This wasn't always the case, however; to paraphrase from memory: "So I was walking along one day, and suddenly I saw this THING, and it was UGLY! It's so ugly that I want to hire somebody to kill it! Blech!"
The game's name generator for NPCs came up with some gems. Players traded screenshots of the best of them, including "Chewibaccabot", "Ape Weenie", and "Boo-Who Adrew".
The game typically used an Invisible Wall to prevent them from accessing NPCs or missions they were not supposed to be able to get to yet. For instance, anyone visiting the Emperor's private retreat on Naboo who wasn't an Imperial who had worked their way up the associated mission tree wouldn't get any further than his secretary, because an invisible wall would bounce them away from the door. The only problem was that a player could, in theory, complete the Emperor's quest line, then quit the Empire and defect to the Rebellion. This would not reset the invisible walls, allowing them to stroll around the retreat and chat up the highest ranking members of the Empire, even while dressed in full Alliance regalia. And what was the Emperor's (or Darth Vader's) response to seeing a rebel agent wandering the halls? A very polite, "Sorry, only Imperial employees are allowed to work for us."
Pre-CU Jedi had to go through a series of Padawan trials, assisting people around the galaxy, in order to prove their worth as Jedi. One of the trials involved assisting a chef in hunting down a pie thief. The correct action to pass the trial was actually to decline to help him (since he wanted the thief killed for his crime), at which point he would moan, "It's not fair. Not at all. I hate everyone."