Well, how I do it is, I have the players create a character and back-story, then I come up with a starting point that relates to the character back-stories in some way or other. Then from there the plot writes itself. When I say plot, I mean 'story-line' rather than any of the word's other meanings.
Best described by example I suppose.
The three adventurers in one of my campaigns were wanted by the local guards. They were spotted by the guards and I placed the guard tokens on the table top. I spoke as the Guards and asked nicely if they would come quietly. The PC's could make any choice they wanted here, I would just adjust the story as we went along anyway. They decided to make a run for it rather than fight and cause more trouble in the village they all grew up in. Now people are looking for them, and they are worried about being caught in the village, but they are also wanting to know why they are wanted. So they need to come up with a plan to find this information, who knows what they will do next! I sure don't!
I have plenty of NPCs that they could approach, though they don't have many allies left in the village and most would alert the guards.
There was hardly any combat, but the players had tense moments and decisions to make throughout the game. Now you might be thinking, "Oh whaaat!? Guards are wools they should have bashed 'em! At least for the XP"
Well if they had attacked the guards, being level 1 would not have helped, since these guards were much higher in level. The guards wouldn't have killed the adventurers but they would have knocked them unconscious and taken them to the prison cells. They would have found out why they were wanted but, they wouldn't have the advantage of being free!
Now, based on what I see on these forums, what I see on other forums, and my own experience checking out pick-up groups online, this kind of play appears to be very common.
My question is this: Is this what your D&D looks like? Have you played in games like the one described? What was your experience?