Now someone jump in here if I forget one....

William I and Richard I were both (blatant?) homosexuals.  This is bad in a king because their primary responsibility is to beget an heir and if they refuse to do so (as in the case with these two) they have failed in one of the primary functions of a monarch.

Edward II and James I were most likely bi-sexual (both produced heirs, so what the heck)!

I think any rumours about Queen Anne being gay would probably have started due to her very close friendship with Sarah Churchill. Her husband John won various battles as a general for the Crown and was made Duke of Marlborough - the couple were the ancestors of Winston Churchill. Anyway, Anne and Sarah were incredibly close, with Sarah very clearly the dominant partner - apparently, she was fairly overbearing and unbearable! - but both husbands seemed happy with the relationship and, has been pointed out, Anne certainly did her dynastic duty (as did Sarah).

Sarah had initially been close to both sisters, Anne and Mary, but moved closer to Anne after Mary married William - a much stronger character than Anne's husband, Greorge of Denmark.

From The Lives of the Kings and Queens of England, ed. Antonia Fraser:

"Her passionate affection for Sarah Churchill, the future Duchess of Marlborough (this at the beginning of Anne's reign), which began before she was married, was to give her (Anne) much pleasure and later much pain. Sarah's voluminous writings have been largely relied upon by Anne's biographers as a basis for assessing her character, but it has to be remembered that what Sarah recorded was chiefly written after they has quarrelled. ... Sarah had given birth to four very healthy daughters which made her feel very supierior to Anne, whom she treated with some condescension. ... When Anne became Queen she wrote to Sarah, whom she appointed Mistress of the Robes: 'We four must never part until death mows us down with his impatial hand.' ... Her alienation from Sarah, which had begun not long after her accession owing to Sarah's haughty attitude to her as Queen, was increased by the fact Sarah absented herself from Court for long periods and devoted herself to pro-Whig propaganda. ... At the beginning of 1711 Anne dismissed Sarah from all her offices after some painful scenes and at the end of the year Marlborough was also dismissed. Anne died on August 1, 1714, still perplexed by the extingencies of party politics."

Lady Grace.