I guess I was getting mixed up with pronouns--which don't require the copula, right? Are they the only thing that doesn't? For example in an "x is y" sentence? Then you have "the x is y" and "the y x," where x is the subject and y is the adjective... right? Guess I need to study more :)
You need a copula when equating a noun to another noun, ספר הוא חבר. You also need it to express that a noun is an adjective, but only when the noun is indeffinite - הספר עצוב would be a whole sentece, the book is sad, no copula necessary, but ספר עצוב is just a noun phrase, sad book.