Eventually I would like to see the quest system expanded on to include things like tutorial quests (build/craft this etc), mini games (racing, ground combat arena etc) and the like, but exploration (go here) and bounty hunting (take out this ship/station) are a pretty reasonable starting point.
Since the quests are going to be based on LUA scripting (if I didn't dream that fact :p ) I imagine a fair few quests will be community generated. The quest system is one of the things I'm really looking forward to seeing come to fruition.