It is a fairly obvious truth that the vast majority of Tolkien's female characters end up married - the two exceptions I can think of are Lady Haleth of Brethil (who made the deliberate choice not to) and Finduilas of Nargothrond (who had two essentially-engagements). It is also true that, while many of his male characters also marry - sometimes to women conjured up solely for that purpose (hello, Diamond of Long Cleave!) - there are a fair number who don't. Obviously, this is unfair, and sexist, and misogynistic. Isn't it?
Actually, I'm not so sure. I don't think Tolkien thought so much in terms of marriages as he did couples - pairs of people who are deeply and intrinsically linked. So where (male) characters don't get married, more often than not they end up in a deep and abiding friendship, or family bond. Some examples:
Legolas & Gimli are possibly the most obvious example of The Unmarried Men - and also the greatest demonstration of what Tolkien was really thinking of. Their friendship, while never suggested by Tolkien to be romantic, is deep enough that Legolas tried to take Gimli over the Sea with him (though whether he succeeded is unknown).
Elladan & Elrohir, the twin sons of Elrond. Have you ever noticed how they are always named together? In all of their recorded actions, they act as a single unit. A different type of pair bond, true, but still just as strong.
Maedhros & Fingon, and later Maedhros & Maglor. This is one of many examples of strong bonds which shift throughout an individual's life (see also: Sam & Frodo, which is replaced by Sam & Rosie, as well as Merry & Pippin who split off to their separate wives before rejoining at the end of their lives); in both cases, the two are willing to sacrifice almost anything for each other.
Huor & Hurin, while both married, clearly share a strong bond of their own.
And the examples could continue (Cel'n'Cur, for instance). Many of these pair bonds are between close relatives, but some cross species boundaries. I don't think Tolkien thought of them as in any way romantic - rather, these were exactly the sort of relationships he had in his own life, with his brother, during the Great War, with the Inklings, and with his wife. To Tolkien, a happy ending - a fulfilled life - wasn't necessarily being married... but it was being part of a pair.