I could see it altering quest dialogue and quest access. Handle quests for a particular NPC often and well, it builds reputation and opens up more and more lucrative quests in come cases, or may open up more fetch and busy quests depending on the NPC as certain NPCs see you as an exploitable resource. Refusing to take certain quests would close them off until you've recovered reputation with that NPC. The early quests you take would help build the network of who you know and what sort of thing you're willing to do for experience and money. It would mean that there may be benefits to actually declining a quest as just taking it blindly and succeeding may close off choices.
If you used a reputation system, you could ultimately take every quest, it just may require some effort to get rep back with certain people. The big thing for me would be being able to have a character built on choices. The problem with something like this is that it's a pain to build and maintain and you'd really want to have this at least somewhat separate from the "main" storyline. So the main storyline are things sweeping enough that even a disreputable sellsword could do.