Languages with multiple forms of the verb "to be"

Interesting question and useful answers. But I'd suggest that the question should really be about the variety of non-verbal predicates across languages. (I.e. She runs. vs. She is young. or She teaches. vs. She is a teacher.)

You will find that languages (even with the Indo European family) vary greatly. Some use a copula in all cases, others only in the past or future or not at all. Some use a copula only for nouns but not adjectives. Some use a simple copula but use a case ending to express the same difference as ser/estar - so called predicate instrumental. Or to express an result such as the predicate dative. Languages differ in how they express definiteness of the non-verbal predicate (e.g. the infamous 'Ich bin ein Berliner.'). I'd say even things like the partitive genitive and other forms of predicative expressions of possession belong here. Things like subjects and locations also come into play (e.g. there is, 'it is cold to me').

In short, limiting yourself to the forms of the verb 'to be' only confuses things because it limits you to comparing things that are superficially alike and exclude things that may be more relevant.