I know that "powerful" is a relative term and that one could ascribe various meanings to it, but let's be conventional here and allow it to apply to sheer combat effectiveness, the way the Gods intended. Naturally, only vanilla backgrounds count. No homemade contraptions in this thread. Personally, I vouch for the Tough Hide background, especially when used by a half-ogre. Being able to shrug off 20% of any physical damage directed at you without wearing a single piece of armour is a great feat indeed. Couple this with Melee and Dodge mastery, maxed Strength, Dex and a good suit of armour and you will be a nigh unstoppable killing machine. Sure, other backgrounds will give you stat bonuses, but you will easily cap the combat-related stats before level 50 anyway. Everything else depends on equipment, and Tough Hide is the only background that enhances that. I suppose Escaped Lunatic would come as a close second.