Sugary things and excess carbs, especially refined carbs. Processed foods. My skin used to be very oily on a "healthy" diet (lots of whole grains, etc), but since eating low carb, whole foods, my skin is very normal, even if I don't wash it in the morning.
Dairy can be a trigger. Cultured or aged dairy isn't as bad. High quality cheese seems to be fine, in moderation.
Too much fiber/anything that irritates my digestive system. This one is huge. Happy tummy, happy skin. If it makes you bloated or causes you pain, don't eat it. Raw brassicas (broccoli, kale, cabbage, etc.) kill my stomach (yes, even though they're "healthy")
Roasted nuts. Only raw is fine for me.
Vegetable oils. If I cheat a little on pretty much any of the above, I usually won't break out anymore, but vegetable oils will get me every time. Soybean, canola, corn, etc.
Most meat, veggies and fruit are safe for me.