Offal, or organ meats, is a foreign concept to most Westernized individuals, who typically opt for muscle meats like T-bones, sirloins, and roasts. Organs are now simply leftovers that are discarded after the animal has been dressed. However, our ancestors and modern day hunter-gatherers opt for the organ meats of animals and have been known to leave behind the muscle meats when food is plentiful. To indigenous folk, the liver, kidneys, heart, brain, bone marrow, kidney fat, stomach, and intestines were all excellent sources of nutritive fat (largely saturated at that). For that very reason, these meats are shunned in the modern low-fat Western diet. Well, that and our general squeamishness.

Nutritionally, organ meats are powerhouses. Liver, for instance, is rich in protein, iron, and the B-vitamins. And if we look at vitamin A, copper, and folate, a 4oz serving contains 610%, 450%, and 215% of the RDA, respectively. Beyond that, it's just darned tasty fried with onions and topped with a bit of mustard. Another beauty of organ meats is that they are cheap, cheap, cheap. That old economic principle of "supply and demand" applies here; since few people eat organ meats, they can be had for a song. Slanker's Grass-fed Meats sells grass-fed beef liver, heart, kidney, tongue, and spleen, all for under $3 per pound. You can also get marrow bones (a good source of CLA) for use in making soup for $1 per pound, give or take. And you can find the organs of pastured chickens and grass-fed lamb, goat, and pig for the same ridiculously low prices.

Below are a few recipes if liver and onions doesn't strike your fancy or if you're looking for ways to spice up these delicious meats. Organs tend to have a slightly sweeter and significantly stronger flavor than muscle meats and may take some getting used to. Most people have had liver at some point in their lives and some probably still hate their mothers for it. Kidney tastes pretty similar to liver. Heart has a flavor somewhere between plain muscle meats and liver, while tongue has the texture of any other muscle meat, though a bit more tender, with a much nicer flavor. Across animal species, organs taste the same, so get whatever is cheapest.

One important thing to note is that organs like liver and kidney are the filters of the body. If you're eating the organs of a grain-fed, antibiotic- and hormone-laden animal, you are getting a super-concentration of these elements. Because of this, it's wise to eat grass-fed organs only. If you get organs from a conventionally raised animal, get calf's liver as it will tend to not have the accumulation of these toxins.

Crockpot Liver with Tomatoes
From About.com

1.5-2 pounds liver, cut in cubes
4 slices bacon, diced
2 small carrots, sliced
2 ribs celery, chopped
1/4 cup chopped onion
1 can (14.5 ounces) stewed tomatoes
1/4 teaspoon pepper
1 bay leaf

1. Place liver in slow cooker.
2. Cover with bacon.
3. Combine remaining ingredients and pour over liver.
4. Cover and cook on low for about 6 hours.
5. Remove bay leaf before serving.

The only caveat on this recipe is to make sure you fill the crockpot sufficiently to keep it from burning to the sides (voice of experience). If you're using a large crockpot (5.5qt+), you will probably need to double the recipe to make sure there's enough food in it.

Kidneys with Onions and Mushrooms

1 lb kidneys
3 tbsp oil
1 large onion, chopped
1 cup mushrooms, cleaned and sliced
1/4 cup red wine

1. Rinse the kidneys in cold water and then soak in cold salt water (1 tsp per quart of water) for 1-2 hours.
2. Remove the outside membrane from the kidneys as well as the tubules from the middle. You'll end up with lots of small hunks of meat.
3. Brown the kidneys in the oil and remove to a plate.
4. Brown the onions and mushrooms until the onion is soft, then add the wine and cook for another minute.
5. Return the kidneys to the pan to warm.

Beef Heart with Mushroom Stuffing
From US Wellness Meats

Mushroom Stuffing:
10 slices bacon, diced
1 medium onion, finely chopped
4 oz fresh mushrooms, coarsely chopped

Beef Heart:
1 beef heart (~3lb, split lengthwise)
3 cloves garlic, minced
1/3 cup olive oil
1/6 cup vinegar
1 cup beef broth

1. Wash heart. Trim fat and remove arteries and soak in cold salted water for 30 minutes. Drain and pat dry with paper towels.
2. While heart is soaking, fry bacon, onion, and mushrooms until onion is softened. Drain grease.
3. Place heart in crockpot and fill heart cavity with mushroom stuffing. Skewer to fasten. Don't be concerned when half of the mixture squishes out the side. Spoon any that squishes out over the top or leave it in the bottom of the crockpot to flavor the gravy.
4. Add garlic, olive oil, vinegar, and broth.
5. Cover and cook on High for 1 hour, then on Low for 6-8 hours.

Beef Tongue

1 tongue, 2-3lbs
Water
1 tbsp salt
1 bay leaf
1 onion, sliced
1 stalk celery, chopped
1 sprig parsley

1. Place tongue in kettle and cover with water and add remaining ingredients.
2. Cover kettle, bring water to a boil, then reduce to a simmer until tongue is tender, or about 1 hour per pound.
3. Remove from stock to cool. Remove skin and roots from tongue.
4. Slice and serve with mustard and/or horseradish.
5. Save the stock for soup.

For easy vegetable soup, take the stock from the beef tongue, throw in a pound each of straight marrow bones, knuckle marrow bones, and meaty soup bones, add vegetables of your choosing, and you have vegetable soup full of marrow-y, meaty goodness. These recipes are just one example of ways to use each organ. Google is a rich resource for finding recipes for these meats, including the British treat Steak and Kidney Pie (it's even Paleo if you avoid the crust). US Wellness Meats also has several recipes for liver, kidney, and heart here.

References
http://www.westonaprice.org/traditional_diets/native_americans.html
http://www.whfoods.org/genpage.php?tname=foodspice&dbid=129
http://www.grasslandbeef.com/meat_descriptions.html