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In the series finale of Voyager, we see

the Borg collapsing as the queen dies due to the virus that the future Admiral Janeway infected them with.

However, were the Borg destroyed or did the virus just cripple the base and cause mass casualties? I've been unsure of the Borg. Sometimes it is implied that the Borg Queen is an actual being who was once one person but enslaved many under a collective consciousness that they guide. Other things tend to imply that the queen is the incarnation of that collective consciousness. So if it truly died I would imagine that everyone would be "released". Either the collective consciousness would die thereby killing everyone, or their dictating leader would die causing them to be freed from mind control.

I don't know if anything ever says what happened. The movies never go into this, and Deep Space Nine pretty much dodges Borg encounters.

The Borg Queen was likely destroyed, but this doesn't mean the Borg were destroyed

We see the Borg Queen losing her limbs and her connection to the collective. However, we know that this doesn't amount to the destruction of the Borg. As pointed out in @jim's answer, the Queen is destroyed in First Contact (set in 2373) and then reappears in VOY ('Endgame' is set in 2378). Furthermore, the Borg obviously still exist in VOY after the Borg Queen has been killed in First Contact and is 're-incarnated' for want of a better word.

The only further reference we have to the Borg in canon is in Star Trek Countdown 3 where we learn the Narada was retrofitted with Borg technology. However, this doesn't tell us anything, other than that Borg technology still existed.

So, to speculate

Memory Alpha tells us that the Queen's function is to order the Borg, so her removal would undoubtedly cause chaos for the Borg. However, the events of VOY following First Contact would indicate that she can be replaced.

The destruction of the Unicomplex we observe is likely because that is where the Borg Queen controls the Borg; without her, it is likely to crumble. We know that the Borg can repair their ships through thought, so the absence of the Queen resulting in the destruction of the Unicomplex is no surprise.

The agent that Admiral Janeway used to achieve all of this was a neurolytic pathogen, which, based on MA's description, likely only affected the Borg Queen and her control over the Borg.

So, based on this, my expectation would be that NO: the Borg were not destroyed at the end of Voyager, merely set back a fair way with their transwarp hub.

For a non-canon answer, the Star Trek: Destiny trilogy of novels, which takes place about eight years after the events of Nemesis, deals with the final disposition of the Borg (as well as their beginning) in a satisfying way IMHO. I throughly enjoyed these officially licensed novels and highly recommend them, even though they aren't officially considered "Canon".

Not only has the Borg Queen been destroyed at least twice (in First Contact and Endgame), another version appeared in Voyager, "Dark Frontier" and "Unimatrix Zero". It isn't clear if this was meant to be the same Queen in all cases.

There were six transwarp hubs in the Milky Way galaxy.

There are multiple queens. The queens are also grouped into a hierarchy. They act to organize and process the collective. Each ship has a Borg queen. Each unimatrix has a queen, and of course their home base that Admiral Janeway destroys during the season finale of VOY has the top queen.

The queen (you never see but hear about during First Contact) during "Best of Both Worlds" dies when that ship is destroyed. The top queen is killed during "Dark Frontier" on board her personal craft. Even though it was the same actress in "Unimatrix Zero", it is a different queen.

The top queen during "Endgame" is the current top queen. Two times in the Star Trek world you see when the queen is killed so are the drones under her. It would seem that the Borg are destroyed at the end of "Endgame", however, even if one ship survived with its queen still alive, that ship would still be enough to assimilate and start regrowing.