Semantical notes
Linguists call the verb "to be" a copula, when it indicates identity, belonging, or the possession of attributes; that one thing is a special case of another, or that it simply is anything. One can distinguish, as logicians do, the possession of attributes from class membership. We can, therefore, identify four senses of "be" and its conjugations.
Usage in different languages
No known natural spoken language lacks irregular verbs entirely.
Most often, "to be" has the greatest difference from other verbs.
Because speakers use it so often, it tends to change more slowly than the rest of the language and thus falls out of the "regular" pattern that most other verbs show.
Even the extremely regular agglutinative Turkish language forms its "being" verb differently from other verbs.
In Indo-European languages, the words meaning "to be" and "to eat" (originating in stems *es and *ed, respectively) often sound similar to each other. Due to the high frequence of their use, their inflection retains a considerable degree of similarity in some cases. Thus, for example, the English form "is" is an apparent cognate of Russian yest' , in spite the fact that the two belong to language groups that had split at least three thousand years ago and have had very little interaction since (20th century borrowings notwithstanding).
Other languages have multiple words for the verb "to be", dividing its uses in different ways. For example, the Japanese language has two forms: "arimasu" for the existence, and "desu" for identity and the property-possession uses.
The Spanish language also has two words, but divided differently: "ser" for uses expressing permanence (whether existence or attributes) and "estar" primarily for temporary conditions, either of existence or attributes. These are the kinds of issues that make machine translation difficult. For example, the English sentence "I am strong" would become two different Spanish sentences depending on whether the speaker intended to express that this was an inherent quality he possessed ("Soy fuerte"), or a present condition based on circumstances ("Estoy fuerte"). The Portuguese language also has the same distinction between "ser" and "estar".
Finally, the divisions often have exceptions.
To say that "a book is on the table", for example, Japanese would use the "arimasu" form, saying "Hon wa, taberu ni arimasu," meaning roughly "as for the book, there exists on the table", while Spanish would use the "estar" form "El libro está en la mesa", meaning roughly "the book presently possesses the property of being on the table" (this is so even for things that are always where they are - La Torre Eiffel está en París.)
In the Russian language, the verb byt' is the infinitive of "to be." The third person singular, yest' means "is" (and, interestingly enough, it is a homonym of the infinitive "to eat"). As a copula, it can be inflected into the past (byl), future (budet) and subjunctive (byl by) forms. A present tense (yest' ) exists, however it is not used as a copula, but rather omitted altogether or replaced by the verb yavlatsa (to be in essence). Thus one can say: