What do the players want the PCs to accomplish

I don't really recall having much in the way of grand PC-level goals. This was one of the difficult things about trying character play. The satisfactory games tended to be the ones in which what was to be accomplished was limited and tactical — goals like “Clear out the deserted Wiri colony on 3rd level”. Such goals, of course, arose on a player level, answering the question “what do we want to do tonight?”. The episodic nature of the games — dungeoneering, superheroics — lent itself to such tactical play. Adding continuity did tend to replace the answer of “whatever we feel like” with “whatever we were lumbered with as a leftover from last week, again”. This, in retrospect, may not be an entirely unalloyed plus.