Yeah, second for Burning Wheel. Definitely a system I could see running an entire campaign without a single combat encounter and it not being even remotely a problem. I think any game that had a decently robust skill system can be used to run a campaign that isn't combat oriented. The more skills a PC has that relate to things outside of combat the more often a player can roll dice and the more opportunities there are for "things to go wrong" which leads to even greater consequences. I also think theme has more to do with it than anything. The mystery and spy genres are probably the first one that come to mind, though setting and system will inform play. I ran a Star Wars game years ago using D6 SW were the players were members of the ISB. I think there was single instance of combat about midway through, when the players decided to defect to the Alliance. Then of course, the campaign ended with a combat where the PCs sacrificed themselves in glorious fashion to save someone's cheese sandwich or something. I also ran a decently long game of Vampire that had zero combat, mostly because none of the PCs were even remotely the kind of people that would get into a fight, much less a shootout. There was some violent interaction with mortals from time to time, but due to judicious use of Disciplines I would be loathe to call what happened "combat" of any recognizable sort. I have never played it cause I don't really understand the system, but I'm lead to believe that if combat were to occure in Brindlewood Bay something has gone drastically wrong. Tales From The Loop is another one that I think would work quite well with no combat seeing as it has no combat engine, and the PCs are kids solving mysteries 80s movies (Goonies) style. I also ran a dozen session game of MouseGuard one time that only featured a single instance of combat with an agitated Owl that fled after the first round cause the PCs got a good roll and "won" the fight straight away (the goal was to make the Owl flee). MG is BW light, so see above, plus the main "antagonist" in MG is the dangers of travel and the environment so combat is much less likely to occur than in your typical adventure game.
