EDIT Spread
The exclamation mark is used worldwide and has been integrated in many non-latin alphabets. It is part of an international traffic sign and even made its way into 2 City names: it's an official part of the name of the English city »Westward Ho!« and appears twice in the name of a city in Quebec, »Saint-Louis-du-Ha! Ha!«.
In many comics from the middle of the 20th century the exclamation mark is routinely used as a substitute for a full stop at the end of a sentence.
EDIT History
In Germany found for the first time in 1573 in the book »Flöh Hatz, Weiber Tratz« by Johann Fischarts. Used very sparingly, though, just six times in the whole book and omitted in many places where today an exclamation mark would be considered appropriate.
In the 15th century, the exclamation mark was used in a dividing function and usually referred to as »coma«.
It had a surge in popularity during the baroque era, probably because it suited the search for a strength of emotion that was so formative for the era.
In Germany, the exclamation mark was used for different purposes before actually becoming an exclamation mark. It was used for exclamations, but also for calls of surprise, wishes or amazement.
There is a theory that claims the exclamation mark derived from the latin word »io« which is a call of joy. It was used as a combination of the characters i and o or acombination of an i above a dot.
EDIT Typography
The Exclamation mark usually has the same height as a capital letter. The size of the dot below the vertical stroke generally matches the size of the i-dot or a full stop at the end of a sentence. Both parts of the exclamation mark should have a sufficient distance.
The Exclamation mark is put directly behind the last character of a word.
To avoid the exclamation mark clinging to the word and becoming a part of it it may be necessary to manually adjust the distance between word and exclamation mark. Since a full space would be too much it is suggested to put a thin space in between, especially if the font isn't designed well enough to accomodate a bit of space on its own. In display-sized type in particular it is important to check if manual adjustments are necessary.
If an exclamation mark is used after an italicised title at the end of a sentence, it is not put in italics.
EDIT Informatics
The exclamation mark is used in many programming languages. In »c« and other languages it stands for logical negation and is also referred to as »bang«.
In BBC Basic its a substitute for a 32-bit-word and is called »pling«.

EDIT Mathematics In mathematics, the exclamation mark represents a factorial operation.

2! = 1 x 2
6! = 1 x 2 x 3 x 4 x 5 x 6
n! = (n-1)! x n
EDIT Linguistics In the International Phonetic Alphabet (IPA), as used in linguistics to represent the spoken language, the exclamation mark is used to represent the retroflex click, found in various languages in southern Africa. For correct use, it is separately encoded at U+01C3 (Block: Latin Extended-B).