I absoutely must trample any and all opposition. In Arkham City for instance, I go out of my way to fight armed guards. It takes time, and it's risky (somewhat), but I just have to do it, because god damnit, don't you wave yer guns at me! Strangely enough, I tend to ignore unarmed enemies.
In other games, if I come across a foe I can't reasonaby defeat and could easiy bypass, I still have to fight them. Like in Mechwarrior 4: Mercenaries, in Merc Alley B. That ambush cost me 6 tries, and in the end I survived with my 'mech in critica condition, and the rest of my lance destroyed (not dead, luckily). I didn't manage to salvage the enemy Assault 'mech, the weapons I got were shit, and I had no use for a wrecked Argus. But it was oh so worth it. (and your job is actually to run the fuck away)