It is my belief, from personal experience, that a persons sexuality can change.
First, let me state that I am referring to all kinds of human sexuality, not merely the homosexual-heterosexual spectrum. My own experiences deal mainly in changing fetishes and paraphilia; however as what research I've done on the subject seems to exclusively uncover information about gender attraction, I will have to rely on that spectrum for most of the points in this writeup.
The idea that sexuality is fluid seems to be mostly espoused by bisexuals, and those that strongly identify in one of the ends of the spectrum tend to think this claim to be about sexual identity more than about sexual orientation. I've seen claims that "sexual fluidity is really a kind of changing self-assessment against a backdrop of constant but obscured self-nature"1.
I am not going to argue over the fluidity of sexual identity. The answer to this should be obvious. What I question is the assertion that one's sexual self-nature is constant, and that a change in sexual preferences is merely an effect of realizing more about one's own nature. Many such changes are probably products of just that, but in my experience, as well as according to a few other opinions I've managed to dig up, not all are.
If we are to assume that sexual self-nature is a constant, then we can further assume that once a sexual interest or attraction (orientation, fetish, etc) is discovered, it cannot disappear again without resorting to self-deception. My personal experiences contradict this. I have found within myself a number of different sexual urges and fantasies throughout my life, only some of which have remained with me at a fairly constant level since I discovered them. Others have a tendency to fluctuate from weak to very strong, and the rest have largely disappeared from the phase space of my sexual interests. The second, anonymous writeup in sexuality is fluid is another example of a fluctuating sexual interest, in this case the interest in other men.
With these two examples of sexuality that changes and fluctuates both ways, the conclusion is that sexuality is not necessarily set in stone, and that whatever one's sexual nature is, it is prone to change over the course of a life. It is not a far-fetched hypothesis, then, to claim that sexuality can be changed willingly (or even forcibly, though trying to do so would be is reprehensible). If the cause of such a change could be found, it should be possible to "artificially" modify a persons sexual desires.
I do however think it possible, and indeed quite likely, that whatever desire is to be modified needs to be present in a person in some degree beforehand. It may well be impossible to induce a sexual interest in men in a man who has no attraction whatsoever in other males. I also suspect that "core" desires, desires considered by the person to be the most important part of their sexuality, is a lot harder to change. Still, from personal experience, I know even these can change in intensity, and so not even these should be entirely impossible to modify.
Note: After thinking about it, I have concluded that the above does not in fact cover my views on the subject matter very well. I'll leave it as is, with this added paragraph and a much vaguer conclusion; The sexuality of some people can change. I find it likely that it is possible to modify some of the sexuality to most people at least to some degree. Still, some aspects of some peoples sexualities may be entirely biologically determined, or for other reasons impossible to change.
1 http://www.yawningbread.org/arch_1998/yax-100.htm