I eat a cold breakfast unless it's a layover day--in the latter case I make a cup of hot tea. Generally it's cold cereal (muesli or Grapenuts) with extra nuts and freeze-dried berries (or fresh in season) added, plus about 1/4 cup dried milk. I add water, stir, and eat. Although I consider myself a coffee addict at home, I get along fine without it on backpacking trips.

One reason I go without coffee when backpacking is that dried milk heated in coffee tastes terrible (to me,anyway) and leaves a mess to clean up. With tea, all I need to do is rinse out the pot with no more than 1/4 cup water. With water (which is what I drink most of the time), I don't even need to do that, or use the pot at all. The cereal is in a plastic bag, so when I'm done there's just a tiny amount of garbage and my spoon to lick and rinse.

I have, a few times, eaten cold, uncooked dinners. Usually that has been when I'm too tired to think about breaking out my stove. At least once, I just ate a couple of cereal bars plus a little dried fruit and nuts (my normal "lunch") and then crawled into my sleeping bag. There are some foods that can be rehydrated with cold water, although you may have to start at noon and carry the water for the rest of the day. You'll want to experiment at home with the specific foods before trying this out on the trail.