True they're part of that debate but I don't think it's a lens hood vs no lens hood debate, it's a filter vs no filter debate (with the no filter crowd, including me, pointing to lens hoods as good protection to counter that rational for using UV filters.)
To throw in my 2c to the OP's question (in case it wasn't obvious): lens hood, lens hood, lens hood!

The only time I don't have one on is if I don't have a hood that fits that lens (like my 55mm F1.2), in which case I'll usually try to hold my hand over the edge of the lens to accomplish the same result (and I will put a hood for that lens on my to-buy list!) For flash, I usually will use a hotshoe or wireless flash if the lens hood is in the way... I rarely use the onboard flash.
Put it this way - the lens hood will never make your photos look worse, it can only make them look better. (Unless you are deliberately going for a "look" with low contrast and lots of flare.)