For me, 50mm +. Anything less is skinny. I don't care about speed and riding long distances bores the hell out of me. Getting out on my bike and going wherever my impulse takes me is my preferred riding style and fat, cushy tires give me the versatility to do that. I'm to the point where the deciding factor on purchasing a bike is tire clearance. If Schwalbe made a 3" Big Apple, I would be upgrading to a frame that can fit those.
This is a good template, but with regular MTB handlebars:
This is what I'm currently riding:
