As an additional note to the
writeup by
Jeeves,
desu is in fact, more
regular than it appears.
The conventional form "desu" is a contraction of the form "de arimasu" or "de aru". This form is often considered more literary, and is commonly found in books, dissertations, theses, etc.
"Aru" however, has an irregular negative conjugation, that is, "nai" (in the plain form). The form "dewa arimasen" which is used for the negative of "desu", is therefore a slightly irregular negative conjugation of "de aru" with the particle "wa" inserted.
Ergo: de aru -> de wa nai
The form "deshou" has the plain form "darou". This form is sometimes called the suggestive, because it is variously translated as "you see", "isn't it", "probably". Because this form expresses more than just "desu", it is used to soften sentences, sometimes in effeminate speech.
The particle "no" is also often prefixed to desu to form something called the demonstrative. Used in this way, "no" is sometimes shortened to just "n". This form expresses something of an explanation.
Jikan ga nai n desu yo
I don't have time, you see.
Jikan ga arimasen
I don't have time.
As you can see, these various forms are hard to translate, and sometimes are ignored, leaving very wooden translations.
Also, fans of samurai/Edo-jidai cartoons may be interested to note that "de aru" is the origin of the form "de gozaru"/"de gozaimasu". Gozaru is the irregular honourific that is used in place of aru.