First we must make a distinction between two types of multilingual corpora: the first can really be described as small collections of individual monolingual corpora in the sense that the same procedures and categories are used for each language, but each contains completely different texts in those several languages. For example, the Aarthus corpus of Danish, French and English contract law consists of a set of three monolingual law corpora, which is not comprised of translations of the same texts.
The second type of multilingual corpora (and the one which receives the most attention) is the parallel corpora. This refers to corpora which hold the same texts in more than one language. The parallel corpus dates back to mediaeval times when "polyglot bibles" were produced which contained the biblical texts side by side in Hebrew, Latin and Greek etc.
A parallel corpus is not immediately user-friendly. For the corpus to be useful it is necessary to identify which sentences in the sub-corpora are translations of each other, and which words are translations of each other. A corpus which shows these identifications is known as an aligned corpus as it makes an explicit link between the elements which are mutual translations of each other. For example, in a corpus the sentences "Das Buch ist auf dem Tisch" and "The book is on the table" might be aligned to one another. At a further level, specific words might be aligned, e.g. "Das" with "The". This is not always a simple process, however, as often one word in one language might be equal to two words in another language, e.g. the German word "raucht" would be equivalent to "is smoking" in English.
At present there are few cases of annotated parallel corpora, and that which exists tends to be bilingual rather than multilingual. However, two EU-funded projects (CRATER and MULTEXT) are aiming to produce genuinely multilingual parallel corpora. The Canadian Hansard corpus is annotated, and contains parallel texts in French and English, but it only covers a restricted range of text types (proceedings of the Candian Parliament). However, this is an area of growth, and the situation is likely to change dramatically in the near future.