Common Behavioral Problems
For ease in identification, I'll try to break down these behaviors into categories. I'll add more as they come up in questions, but for now, I'll give you what I can.
The first thing I want to do is remind you that anytime your animal develops a behavioral problem, you should call your vet and talk about it. They have your pet's medical history and know what kinds of medical problems can cause these aberrations in behavior. You must rule out physical causes or find and treat them - because if your pet has an underlying medical problem, behavioral retraining will NOT solve the problem.
Second, I would like to recommend as an invaluable source to myself and this website, the book The Cat Who Cried for Help: Attitudes, Emotions, and the Psychology of Cats by Dr. Nicholas Dodman of Tufts University. This book contains many situations and solutions that may give you ideas in how to solve your animal's problem, including considering when medication is appropriate to treat purely behavioral problems.
What's that? you say. Prozac for kitties? The short answer - yes. There are a variety of anti-anxiety medications available. Why? Because some animals just don't train easily due to stress. An example is a normal, happy dog. You say the word sit, you push down his butt, and you give him a yummy treat. After a couple of times, you don't have to push his butt anymore.
Now, consider the stressed dog. Trust me, you can relate - how hard is it to concentrate on your job when your kids are sick, or you're in a fight with your spouse or a family member? For whatever reason, this stressed dog has all that same kind of "noise" in his brain, distracting him from what you're trying to show him. So, it takes him maybe twice as long to learn to sit.
Now consider the cat. First off, your cat thinks you're a little off for daring to try to train it to do anything. However, even the most arrogant cat can be taught to do a variety of things. Koshka now understands what "come here" means, even though she is kind of tricking me to get food (as in, she knows if she does something bad, I say "come here" and she gets a treat - thereby being rewarded for the bad behavior, in a way). I digress.
Now think about the stressed cat. If you thought you needed patience before - you don't know the half of it. That cat is darn near incapable of clearing out the noise for the length of time that is required just because it's a cat. So the medication clears out the noise for them, helps them relax, and more easily learn what you're teaching them.
This is not to say all cats should be medicated so that we can teach them to sit. :) Medication is still serious, and should only be used when necessary, under veterinary care, and with close monitoring. Then, when weaned from the medication, the training sticks with the pet. Neat, huh?
Determining the Cause (Why are you suddenly acting this way?)
Aggressive Behavior (Ow! Stop that!)
Destructive Behavior (The couch is not your scratching post)
Inappropriate Elimination (Why have you stopped using the litterbox?)
Phobias and Anxiety (Really, I AM planning on coming home later!)