Are we really in control of what we want? What might be the most significant philosophical theories or works discussing this problem?
There are a number of questions here on this site that address this same line of thinking. I would start by reading about the concepts of:
on SEP/Wikipedia, and then search our site for the tag free-will, as well as doing a search for "determinism" and "control". Personally, I think the latter term is key, although not often the focus of modern (NOT contemporary) discussions of free will. I wrote something on that notion in an answer to a few question on this site a few times.
This is a much more appropriate question for cognitive scientists--if cognitive scientists do not know the answer, then we do not know the answer.
It is an empirical matter as to how in control we are, as there seem no logical problems with everything from "complete control" to "no control at all (but perhaps with the illusion of control)".
To convince yourself of this, note that there are aspects of behavior where each seems to be the case. For a control example: in the game Simon Says, people can reliably control themselves from following orders when the order is not prefaced with "Simon says". For lack of control: images with multiple contradictory interpretations (old woman/young woman, dog/rabbit, Necker cube) often generate an illusion of control if you ask someone to try to flip the percept when they feel like it. Typically, people report control, but the statistics of flipping percepts are identical to people who were not attempting control (and if you give them a cue on which to flip, they are unable to).
Having decided that this is an empirical matter, the best thing to do is collect data or talk to those who have.
There's a book on this by William B Irvine, called On Desire: Why We Want What We Want (OUP: 2007).
He engages philosophically with Freud, among others, whose theory of the Unconscious mind implies that we are not always in conscious control of our desires. That doesn't entail, however, that the source of our desires is something other than a part of us.
Humans and other animals have no direct control of what they want. Your "personality" is not a cause in itself, independent from nature. It is very dependent on the wiring of your brain, which again is dependent on the genome and the experience you made throughout your life.
Hence, you can only realize what you want and may act according to it. If you can act on your desires you experience joy, if you cannot you experience distress.
Or as Schopenhauer once said: "Man can do what he wants but he cannot want what he wants."
Also being able to supress certain desires is not a sign that we control our desires, as the desire to control such desires is a desire, too.
That being said, there are ways to train ourselves to behave according to a socially accepted manner, be it through positive reinforcement or punishment. Or by gaining insight for the necessity of (not) doing an action through learning, either by making mistakes in the real world or by making thought experiments. Or by learning how other people did things in the past and prevent us from doing mistakes again.
In my experience we are not in control of what we want short-term, but with knowledge about ourselves and the world around us we can take control of what we want long-term (not in the sense that we can escape cause and effect, but in the sense that our internal workings are consciously influencing the outcome).
Short-term we want what we are programmed to want e.g. if you always thought money would solve all your problems and help you achieve your goals you are likely to want money and find it impossible to say no to it if it was given to you. But if you brainwashed yourself by every day listening to stories about how money is the root of all evil and surround yourself with friends who hate money on principle, then in a few years you might actually say no to money if it is given to you.
So you cannot be in full control of your 'wants' but you can certainly (somewhat) control what you will 'want' in the future by feeding yourself the appropriate information and putting yourself in the appropriate situations for a particular want to shrink or grow.
I think the same mechanisms apply to subconscious wants (which many seem to call desires). This is how we get over our natural instincts to always say yes to fat, sugar and sex, and also how we some times manage to get over addictions. e.g. if you are a smoker you will want (desire) a cigarette soon (rationally you might really really want to quite, but you will still go out of the way to make sure you get another cigarette). But long-term you can 'program' yourself to not even want it subconsciously (or at least stop it from ever being acted upon) by feeding yourself the appropriate information and putting yourself in the appropriate situations for this want (desire) to shrink.
So, Long-term we have the potential to be in control of what we want and desire, but not short-term since it is very hard to change what we want and desire on the fly.
"Are we really in control of what we want?" is a question directly addressed by Harry Frankfurt (of "On Bullshit" fame), who identifies freedom with what he calls second-order desires in his essay Free Will and the Concept of a Person (1971). In this essay, Frankfurt claims that our freedom is contingent on our exercise of desires whose objects are other desires that we have, such as wanting to be free of addiction, or wanting to be motivated to exercise regularly. In this sense, "wanting heroin" can be seen as a first-order desire; "wanting to no longer want heroin" would be the second-order desire. He distinguishes people who entertain these second-order desires from those that don't, to pick out a compatibilistic definition of "freedom" applied to the former.
I can't answer to this being the most significant philosophical contribution, but it's the best fit to your question that I can think of, and still a lively topic. It may help you find the correct stream of argument you're after: just pore through the abstracts of the "works citing this item" list that JSTOR includes. (if you can't access the paper immediately, JSTOR offers a free 3-paper a month download now, for the price of a couple minute's free registration)