Why is a bathroom sometimes called a "john"?

"John" is sometimes used as slang for a bathroom or a toilet.

I'm curious, what is the origin of this usage?

According to Etymonline, the term probably derives from jack or jakes (regardless of the John Harrington angle).

john "toilet," 1932, probably from jack, jakes, used for "toilet" since 16c. (see jack).

Even the article mentioned by @ect says pretty much the same thing:

Around this time, Harington also devised Britain's first flushing toilet – called the Ajax (i.e. "a jakes"; jakes being an old slang word for toilet)

The straight dope has an answer to this question printed in 1985. The origins of referring to the outhouse as "john" or "jake" evidently goes back to the 16th-century.

This is one of those questions for which there isn't a good answer, but let's face it, many is the time I've had to cobble together an answer for which there wasn't a good question. "John," along with an older term, "cousin John," is probably related to "the jakes," which goes back to 16th-century England and apparently is a shortened form of "Jake's house." "Jake" was a generic term for a yokel, but that's about all I can offer in the way of etymological wisdom. Basically, "john" is just another euphemism for an appliance that, as I have pointed out before, is one of the few things for which there is no simple descriptive term in the English language, i.e., one that resorts neither to euphemism nor vulgarity.

FYI, another answer references cuzjohn usage in Harvard regulations, this word is a contraction of the older phrase cousin John which has been shortened in modern parlance to simply the john.

Green's Dictionary of Slang suggests john is possibly short for cuz john, a usage which it dates back to a Harvard College regulation from 1734:-

216:20 No freshman shall mingo against the college wall or go into the fellow's cuzjohn.