I noticed early on in my life that after a good workout, whether it was soccer practice, weight lifting, or later on in life, ultra marathon training, I would always have cravings. I would crave ice cream or chocolate milk quite often. Sometimes it would be red meat (specifically hamburger) and potatoes. Sometimes it would just be orange slices. Now, I don't know how "in tune" everyone is with their body, and I certainly don't think we need to give our bodies anything they "ask" for (I have heard of women in pregnancy craving dirt or clay), but I have always interpreted these kinds of cravings as my body's way of telling me what it needs. The tricky part is trying to learn to separate what it really needs from what you think it wants.
When the body has been pushed to work harder than normal, it has no doubt been depleted of important nutrients. For a very simplistic view of what goes on next, let me explain it this way. The body recognizes it is low on these nutrients, and I believe the first response is for the brain to send signals out by way of what we call "cravings." This isn't a scientific article, but I believe it is safe to say that if you ignore the craving stage, the next response is for the body to start responding with noticeable signs of fatigue, cramping, headaches, and other types of discomfort.
Here is what I have came up with for my own specific cravings (again, this is not meant to be a scientific article, so I will try to keep it simple):
Milk - There are some very important vitamins found in milk that our body uses up during a workout. Among these are calcium and vitamin D which are vital to a healthy skeletal system. Milk is also a good source of protein which our muscles need. However, due to the high amount of calories found in dairy products, you may opt for some other sources of calcium. Also, many people have a low tolerance for dairy. Some alternative sources include: dark green vegetables (like collard greens, kale, okra...), plant milks (soy milk, rice milk, almond milk...), other grains, fruits, and vegetables (do a little research to find many more options if you would like).
Chocolate - Often my personal cravings are not just for milk, but chocolate milk. I believe the reason for this has a lot to do with the sugar (glycogen stores are depleted from your muscles and liver during vigorous exercise). The lactose found in dairy products itself is a form of sugar that can help replace the glycogen stores, but the chocolate syrup will break down even faster. Interestingly, many studies have shown chocolate milk to be the ideal sports drink. On occasion, I substitute with chocolate soy milk as I'm a big believer in plant based proteins (not to underestimate the protein found in meat and dairy).
Potatoes - All carbs break down into sugar, so breads or potatoes, etc. are a way to supply those carbs. Once again, if you are watching your weight, you may want to be careful as many starchy foods (especially if fried) will really pack on the extra calories you worked so hard to burn. Keep your portions small, you probably need a lot less than what your cravings are telling you.
But not only do I crave potatoes, it is usually a craving for fried, salty potatoes (like French fries or potato chips--probably the worst thing for your diet). Salt is a much needed electrolyte and your body loses a lot when you sweat. This is why sports drinks have a lot of salt in them. Normally, it is healthiest to reduce the amount of salt you consume, but during and after a workout, it is natural for you to need a bit more. Again, just don't overdo it.
Red meat - There are three things I think my body is looking for when it craves red meat: protein, iron and just plain calories. Red meat is also usually cooked with a lot of salt and we've already covered why your body might crave salt. Being high in calories is not a bad thing if you really need them. However, you can easily get 1,000 calories from a big portion of steak. You would have to run 10 miles to burn that many calories! So, once again, remember to keep portions small. As for the protein and iron, red meat can be a great source of these, and I do recommend it in moderation.
Secondary sources that replace red meat would be soy (or tempeh) and tofu. These are excellent sources of protein and iron. They also contain a whole lot less calories. In fact, you may consider making them your primary choice...but if you are like me, I just like red meat!.