The Borg have 2 goals, in my opinion.
to obtain perfection, either biologically, or technologically. This goal is something that may or may not even be accomplished, as the further you improve, the more you may understand, and realize you can improve further.
To create order out of chaos. This seems to be the underlying goal, to their quest for perfection.
Seven of Nine: 300,000 individuals have been transformed into drones. Should they be congratulated as well?
Borg Queen: They should be. They've left behind their trivial, selfish lives, and they've been reborn with a greater purpose. We've delivered them from chaos into order.
Source: IMDB (Internet Movie Database)
In 2378, a crippling blow was delivered to the Borg when Voyager discovered one of their transwarp hubs and destroyed it, killing the Borg Queen (again) and devastating the Unicomplex in the process. During this battle, the Borg were infected with a neurolytic pathogen, which was carried by Admiral Janeway and designed to disrupt the hive mind, to bring chaos to order. It was this pathogen that killed the Borg Queen, and allowed Voyager to destroy the transwarp hub.
Source: Memory-Alpha
To create order out of chaos is a massive goal, and is not contained to simply our galaxy, but the entire universe. Given the chance I believe this is the Borgs end game, to attempt to bring order to the whole universe, something that may very well be impossible, but would be a worthy goal to work toward indefinitely.
For what can bring order out of chaos? Why, only a perfect entity of course, The Borg.
