The Borg Queen said:
If you ignore the whole "poor writing" aspect of the Borg, that is...
Because they believe in perfection, to the point of wanting to "perfect" the whole galaxy (if not the universe) so they want to assimilate other cultures in order to do this (cloning wouldn't accomplish this.)
Voyager fucked this idea up, much like they fucked a lot of things up, but I had the theory that the Federation was the reason why the Borg went from simply being machine-like beings whom Guinan suggested it was possible to reason/align with to the assimilators we see through the rest of the time we see them.
The Borg are, pretty much, the "anti-Federation." Before encountering the -D in System J-12 they were just a race that adapted machinery with biology and they did the same with the 12 they took from the -D. Well, when they began aquiring the minds and thought patterns of those 12 they got the ideals of the Federation (galactic unification) and took it to a twisted extreme. Kind of the way some may look at the Federation and how they "assimilate" races and neutralize them into "one race." So the Federation is, indirectly, why the Borg started assimilating.