Breakfast can be a variety of things. For many hikers, the first choice is to go with something like cereal that requires no cooking. That enables you to save weight on the fuel you need to carry for your stove. However, if you are on a long hike, or you are at higher elevations where it can cool down significantly at night, the occasional hot breakfast is a great way to start the day. Oatmeal is an old standby that doesn't require too much cooking or cleanup. Consider flavoring it with something like maple syrup (repacked in a plastic bottle).
There are also some excellent freeze-dried egg combinations available at specialty outdoors stores. If you go for one of these, try to get one of the types that cooks in the pouch, instead of one that you need to cook in a pan. That will save on cleanup time.
For many hikers, lunch is something that is eaten on the go. A squeeze tube filled with peanut butter is one simple option. Supplement that with GORP (good ol' peanuts and raisins). A good GORP mix can also include other nuts, like almonds or walnuts, as well as something sweet, like M&Ms, which won't melt in your pack.
Jerky is another lightweight option that works well for lunch.
For shorter trips, or trips in colder climates, cheese is another option. Sharp cheddar will keep for a while, even under standard trail conditions, but it will eventually get moldy.
Trail bars, such as PowerBars and Clif Bars, are also a great trail snack that doesn't take up too much space or weight.
Dinners should be tasty and provide a lot of calories and nutrition. Instant soups are a great starter and a welcome way to warm up if it's gotten colder at night. Add some olive oil to flavor the soup more and provide extra calories.
For a main course, freeze-dried meals that cook inside the pouch are a great way to go. They taste good and don't require a lot of cleanup. However, they are somewhat expensive. Your local grocery store probably has a lot of options, such as instant pastas or instant rice dishes, that will also work well. Again, you can add olive oil or even butter (repackaged in a squeeze tube) for more flavor. Instant mashed potatoes are another great option, and they can also be cooked for breakfast.
Carry a variety of hot drinks as well for both dinner and breakfast. Herb teas and hot chocolate are a great choice. Some hikers like to drink coffee as well, but be aware that coffee can dehydrate you.
Energy gels such as Gu can provide a great burst of energy when hiking. Carry a few of these to supplement your trail snacks.