Cats are not the social creatures that humans and dogs are. I am not saying they do not interact with us, I am saying that unlike humans and canines, in the wild they do not live and work in groups or packs. They are territorial and keep to themselves. This means they did not spend several million or more years honing the skills used in a group hierarchy to give and take orders. They developed a totally different set of communication skills that are about a foreign to humans as you can get.  My hope is to try to make you more aware of some of the most common ways a cat will communicate with you. Perhaps after reading this and watching you cat you might just find out he/she has been saying something you have been missing all along.

Voice
In the wild, cats do not vocalize as a general way of communication. But 8,000 to 10,000 years of domestication have helped cats along in this area. Modern domesticated cats have learned that humans vocalize and they have learned to do this as well. How may of you have cats that will mew repeatedly when they want to go out a closed door, get some food or to play? Because humans respond more readily to this, it also reinforces the behavior in your cat.
There are no set rules on how a cat will vocalize, so it is up to you to carefully watch your cat and listen to the sounds he makes to determine a likely meaning. This is not a hard part. Most cats will not hiss and spit in your face to say they like you and would like a meal. But you can read their body language with the sounds they make to get a better feel on what they are trying to tell you. It will jut take some time and patience, but most cat owners will figure out the nuances of their sounds.

Eyes
Have you ever had someone tell you that they do not like cats, or do not want them to come to them, but when they go to someone's home who has cats, the cats will come over and rub against them or sit in their lap? It is really rather funny when you realize that this person was likely speaking with body language to the cat and was telling the cat that they are friendly and like cats.

Consider this scenario: Tom goes to a dinner party at a friend's home. 8 people are sitting in the living room when a cat enters the room. Tom is the only one there who dislikes cats or is allergic or something, and just does not want the cat to come to him. The other 7 people just love cats and want the cat to come to them. The cat walks into the room a ways, looks all around and then walks straight to Tom.

Humans like to make eye contact, especially when you are interested in someone. But cats use eye contact as a way to assert dominance as a rule. The longer you look directly at them the more threatening they assume the gaze is. Tom, not wanting anything to do with Fluffy was likely avoiding eye contact and blinking more often. This told Fluffy "Hi there! I am not a threat at all and do not mind your company". So if Fluffy was to decide to visit someone in the room, Tom was the likely candidate.

Tail
You can use a cat's tail to get a read as well. If a cat is twitching his tail he is most likely agitated. Now would not be a great time to grab the cat and hug it. Thumping of the tail is a sign the cat may be ready for a fight. If the cat drops it's tail down to the floor it may be afraid. If the tail is up and the top is bent (I call it a question mark tail) then the cat is content, happy, curious.

Ears
If your cat flattens his ears then he is ready for a fight. If you are playing with, petting or brushing your cat and his ears flatten, be smart and pull your hand back and give your cat some space. Allow him to calm down. Most people never notice the ears before their cat strikes. They just know they were petting Fluffy and/or rubbing his tummy when suddenly and for no reason Fluffy scratched and/or bit. More than likely Fluffy used his tail and or ears to tell his human friend that he did not want the attention, but his human friend failed to hear the cat speak.

Tummy
If your cat rolls over and exposes his tummy to you, he is relaxed. Keep in mind it may not be an invitation to rub your cat's tummy, that may make him feel vulnerable and may spark a reaction that you do not like. Some cats may not mind having their tummy gently rubbed (my cat Nova loves this), others do not like it. Remember, their underside is a vulnerable area. Little bone protection and a great kill spot. Cats are hunters, they know this. Make sure you do not over step your invitation if they expose their tummy to you. If you have an urge to extend your arm to them, allow them to smell your hand, then gently touch their head. If they remain with their tummy exposed, over time you can try to move your hand closer and eventually to gently rub them there. Just do not be surprised if they do not react as you would like.

Head Butting and Rubbing
Head butting is a way a cat will show affection towards a human or another cat. It is also a way to mark you with pheromones. This allows them to give you a familiar scent as well and a scent that tells other cats "Stay away, this is mine".

Kneading
Most cat owners have likely had first hand experience with this action. When a cat rhythmically presses their 2 front paws into you it is called kneading. This is a throw back from kittenhood, when they would knead at their mothers nipples to stimulate milk flow. As an adult it is a sign of deep affection, not that Fluffy wants you to lactate. It can be annoying if you are not one to properly trim your cat's claws. But try not to push your cat away or yell at him. How would you take it if you walked over to your significant other and kissed them, then they pushed you away and said "No! Bad Frank! Bad!". If you cat's claws hurt, they to grin and bear it, then later that evening go and trim Fluffy's claws. Just do not be mean about it. He was only telling you how much he loves you.

Licking
Mother cats groom their kittens to keep them clean and healthy. It also builds a bond with their kittens. This is often continued when they grow up and they may lick you to build a bond and/or mark you with their scent. Consider this an act of affection and like with kneading, try not to push our cat away.

In General
Keep in mind that my opinions of a cat's communication may not perfectly match yours. Also the communication modes are become modified by us as well. If every time your cat licks your hand you give him a treat, pretty soon the licking is not as much affection as it is begging for a treat. People tend to believe cats are difficult to train, but nothing can be further from the truth. The first section on verbal communication if proof.

I am not a veterinarian or animal behaviorist, so please do not take my information as pure fact. If you have questions, ask your vet. If you take a good eye for details and time, carefully watch your cat and try to figure out his communication. Use what I have told you as a starting point and before long you will have a far better understanding of your cat's language.