Adobo is one of the most quintessential dishes of Filipino home cooking, and apparently originated from a Spanish/Mexican dish known as adobado, which used red wine, which was (and arguably still is) unavailable in the Philippines except at great cost. Some improvisation substituted locally available ingredients for that and others, and came up with a unique flavor that is both sour and salty. This recipe is the type I prepare for myself and my girlfriend from time to time. Ingredient sizes are approximate, of course, adjust to your taste.
1/4 kg. pork or chicken
1 1/2 cups white vinegar
1/4 cup soy sauce
1 tsp. whole peppercorns
3 garlic cloves, minced or crushed in a press
1 red chili pepper, sliced
1 bay leaf
1 tbsp. vegetable oil
In a medium saucepan, combine the vinegar, soy sauce, peppercorns, garlic, chili, and bay leaf and mix well.
Marinate the pork or chicken in the vinegar mixture for at least two hours at room temperature (in colder climates than that of the Philippines, this must probably be done a lot longer for the full flavor to enter).
Boil the marinade and meat mixture over medium-high heat until most of the liquid has evaporated, turning over the meat as necessary.
Mix the vegetable oil in and stir fry for about two minutes.
Remove the bay leaf and serve with rice, whole tomatoes, and salted eggs.
The vinegar used here is white sugarcane vinegar, which is the most common type to be found in the Philippines. Other types of vinegar may work, but might have some odd effects (apple cider vinegar for one leaves a funny taste that doesn't quite complement the flavor of the meat).
As has been noted, adobo is resistant to spoilage even without refrigeration, and the flavor distributes and strengthens the longer it stands. The residue that this method of cooking leaves is very tasty, and can be used to fry rice afterwards, producing adobo fried rice. The same method can also be used to cook swamp cabbage (kangkong), potatoes, and other vegetables. Contrary to what some of the other wu's claim, I've never heard of adobo cooking applied to beef, but I imagine that doing that would not result in adobo but what is more traditionally called beef tapa.