Some people, myself included, use the word they as a singular gender-indeterminate pronoun, instead of defaulting to he, or using he/she, or expanding with he or she, or other new-age pronouns like zie, sie and hir.

From a usage note in the American Heritage dictionary:

The use of the third-person plural pronoun they to refer to a singular noun or pronoun is attested as early as 1300, and many admired writers have used they, them, themselves, and their to refer to singular nouns such as one, a person, an individual, and each.

W.M. Thackeray, for example, wrote in Vanity Fair in 1848, "A person can't help their birth," and more recent writers such as George Bernard Shaw and Anne Morrow Lindbergh have also used this construction, in sentences such as "To do a person in means to kill them," and "When you love someone you do not love them all the time."

The practice is widespread and can be found in such mainstream publications as the Christian Science Monitor, Discover, and the Washington Post. The usage is so common in speech that it generally passes unnoticed.

However, despite the convenience of third-person plural forms as substitutes for generic he and for structurally awkward coordinate forms like his/her, many people avoid using they to refer to a singular antecedent out of respect for the traditional grammatical rule concerning pronoun agreement.

No one is willing to dispute this, are they?

"They" is sometimes used as a third-person singular gender-neutral pronoun. Some grammar mavens may disagree, and consider the construct to be vulgar. Other insist that concern over using "they" in a singular context is pedantry. Some even consider the condemnation utterly incorrect as most grammarians who denounce the use of "they" in the singular are basing their judgement on the rules of the Latin language.

In any case, the lack of a widely accepted, formal set of gender-neutral pronouns poses a significant burden on the English writer. The use of "one," "he or she," or "he/she" are often awkward, particulary when they are used repeatedly. "It," when applied to a person is dehumanizing, and the classic form, "he," is often seen as sexist as well as being awkward in some situations. Many notable writers simply fall back on the commonly used "they."

Besides the Oxford English Dictionary, and the King James Bible, the use of "they" in the singular appears in the works of the following authors (compiled by Henry Churchyard):

Geoffrey Chaucer, Edmund Spenser, William Shakespeare, Jonathan Swift, Daniel Defoe, Frances Sheridan, Oliver Goldsmith, Henry Fielding, Maria Edgeworth, Percy Shelley, Lord Byron, William Makepeace Thackeray, Sir Walter Scott, George Eliot (Mary Anne Evans), Charles Dickens, Mrs. Gaskell Anthony Trollope, John Ruskin, Robert Louis Stevenson, Walt Whitman, George Bernard Shaw, Lewis Carroll, Oscar Wilde, Rudyard Kipling, H. G. Wells, F. Scott Fitzgerald, Edith Wharton, W. H. Auden, Lord Dunsany, George Orwell, and C. S. Lewis.

You should avoid this. Yes, Jane Austen and Shakespeare did it. That doesn't mean that you have to. Linguistic fact should not determine stylistic preference. We all know that language changes, and we all know that usage determines what is correct- in the long run. We all also know that Chaucer used the double negative, but we're not about to all start doing none of that. (Anyhow, you're opening up a huge can of worms if you are to begin citing Middle English verse as proper precedent for modern English prose.) There is certainly precedent for using "they" as the third person singular of indeterminate gender. There is even more precedent for using "he". When "they" is used, it is generally used to refer to people in the abstract. It is very easy to avoid this. Almost no one uses it as a generic third person singular in all cases. How does this dialogue sound to you?

"I went to the doctor today."
"What did they say?"

If you insist that "they" is okay for the third person singular, why does this sound so bad? If I were asking the question of a female, I would default to "What did she say?" This way, I can maintain my precious grammar without fear of being thought sexist.

I suggest avoiding the issue entirely by using the plural when you can.

"Everyone is entitled to their own opinion." becomes "We're all entitled to our own opinions." or "All people are entitled to their own opinions."

Language is about communication. In our language, the distinction between the singular and plural is an important one. Let's not lose it. A written language requires some degree of uniformity. The default today in almost every publication and scholarly journal is to not use "they" as the third person singular. Respect that. Spoken language and written language are different beasts with different purposes.

The only thing worse than a pedant who insists that everyone follows the rules, is the pedant who insists that there are none.