It's only "standard" in North America. Other parts of the world use "A4" size paper, which is 297mm by 210mm. The ISO 216 paper standards are designed to be half the size of the last one, so for the A series:

• A0 - 841x1189
• A1 - 594x841
• A2 - 420x594
• A3 - 297x420 (small poster size)
• A4 - 210x297 (similar to letter sized)
• A5 - 148x210
• A6 - 105x148
• A7 - 74x105 (recipe card sized)
• A8 - 52x74
• A9 - 37x52 (small flashcard sized)
• A10 - 26x37

There is another series, the "B series". It follows the same pattern of halves, with B0 being 1000mm x 1414. Personally, I use B5 (176x250) with my students since it fits into most of their notebooks easily without having to be folded.

The ISO 216 standards for A series papers are:

• the length divided by the width is 1.4142, or a ratio of 1:root2.
• the A0 size has an area of 1 square meter.
• Each subsequent size A(n) is defined as A(n-1) cut in half parallel to its shorter side.
• The standard length and width is rounded to the nearest millimeter since the square root isn't always a whole number.

The B series has the same aspect ratio of 1:root2, but it was designed to cover sizes that the A series didn't cover. Therefore, B series papers are actually the geometric means of A(n) and A(n-1). As I suck at math, you can look up the rest if you're really keen on it. But the point being that a B4 paper is going to have a longer short side than an A4 and a shorter long side than an A3.

As far as when did these standards come into place, they came into effect between 1975 and 1995. There is also a C series standard for envelopes that follows similar principles of geometric means.

Back to your original question about letter sized paper. See ANSI/ASME standard Y14.1 which defines 8.5x11 as the standard, or ANSI A. The ANSI made a similar system as the ISO standards, except since it started with the 8.5x11 already, the aspect ratios of the different papers are all different. As far as WHEN did it become the standard, the best source I found was the American Forest and Paper Association that says that when Reagan became President, he switched the government to 8.5x11 from 8x10.5. Most businesses were using 8.5x11 and the government wasn't, and Reagan switched it. So, I'd say that it became "standard" (private business AND the government, everyone was using it) in the early 1980's.

This also coincides with the rise of personal computers and printers and the death of the typewriter. There were plenty of other paper sizes, namely the Monarch (7.25x10.5) or 6-3/8x8.5, for personal stationary. With less people handwriting letters, or even typing them on a typewriter, more and more people simply use letter sized printer paper for everything.