Let's make two points first regarding self-studying for AP exams: 1.) It is possible to take the AP exam without taking the course; 2.) It is not necessarily in your best interest to take this route. The latter point is one you should pay more attention to because self-studying an AP generally means that you won't learn the topic to the extent that you would have over a year-long class and there is the chance of doing worse than intended on the exam.

Nonetheless, taking the AP without the class is a viable option for the ambitious student. Basically, colleges award credit contingent on your taking the exam and not the class. Your school will offer the classes that prepare you for the exam but your school only serves as an intermediary test-taking center to administer the exams in the spring. That means that you are technically allowed to sign up to take AP exams in whatever subject you want through your school. Even if your school does not allow you to do this, you can always sign up at another school - remember, schools are just test-taking sites for the AP exams.

Every AP can probably be self-studied, but some APs are generally known to be easier than others to plow through and achieve a high score. These include AP Environmental Sciences, AP Statistics, and AP Macroeconomics/Microeconomics. I personally also studied AP Physics B and AP United States History. Your choice of which APs to self-study depends on how much effort you are willing to put in and where your interests lie - it would be a pain to self-study AP English, for example, without any interest in the topic.

The most ideal plan for self-studying is to buy a well-known textbook for the course during the fall and then spend a little chunk of time (~30 minutes, perhaps before bed) to read the textbook. During winter breaks and other breaks you can spend more time to self-studying. In the weeks before the AP exam, you would then increasingly rely on review books such as Barron, Princeton Review, or REA.

In reality, most students will end up relying totally on the review books. This strategy, while not optimal, can still yield good results on the AP exams. What's important is that you must have sufficient time to read over the WHOLE review book and do ALL the problems and practice tests. Usually this will guarantee you at least a passing grade (3) and many times a 5 on the AP.

The cons for self-studying, however, are still significant. It does take quite a bit of time and extra work that could be spent elsewhere. Also, it's usually meaningless if you self-study and get a poor exam score since colleges might wonder why you attempted to do so in the first place. Remember that you aren't doing this just for colleges - do this if you have an actual interest in the topic to begin with!

With that caveat, let me just say that no matter where you go, the skill to study independently is absolutely vital, as you will find out quickly in college, where professors expect you to both learn from them and teach yourself.