There have been many standard sizes of paper at different times and in different countries, but today there are two major systems in use: the international standard (A4 and its siblings), and the North American sizes.
The international standard: ISO 216
A size chart illustrating the ISO A series.
The international paper size standard, ISO 216, is based on the German DIN 476 standard for paper sizes. Using the metric system, the base format is a sheet of paper measuring 1 m² in area (A0 paper size). Successive paper sizes in the series A1, A2, A3, etc., are defined by halving the preceding paper size parallel to its shorter side. The most frequently used paper size is A4 (210 × 297 mm).
This standard has been adopted by all countries in the world except the United States and Canada. In Mexico, Colombia and the Philippines, despite the ISO standard having been officially adopted, the U.S. "letter" format is still in common use.
ISO paper sizes are all based on a single aspect ratio of the square root of two, or approximately 1:1.4142. The advantages of basing a paper size upon this ratio were already noted in 1768 by the German scientist Georg Lichtenberg (in a letter to Johann Beckmann). In the beginning of the twentieth century, Dr Walter Porstmann turned Lichtenberg's idea into a proper system of different paper sizes. Porstmann's system was introduced as a DIN standard (DIN 476) in Germany in 1922, replacing a vast variety of other paper formats. Even today the paper sizes are called "DIN A4" in everyday use in Germany.