I was watching TNG : The Best of Both Worlds, Part 2. The Battle of Wolf 359 resulted in over 11,000 Federation deaths and the loss of a Borg Cube with its crew of thousands of drones.
This led me to thinking, what is the bloodiest war involving the Federation?
Nearly a billion Cardassians and an unknown (but high) number of Federation citizens, Klingons, Romulans, Jem Hadar and Breens died in the Dominion war.
For the record, the largest set of casualties resulted from an attack by the Jem Hadar on their own former allies, the Cardassians.
The Borg invasion of Earth seen in Star Trek: First Contact is known to have resulted in over 9 billion humans being assimilated into the Collective.
In 2366, a Husnock warship destroyed the Federation colony on Delta Rana IV. Unbenknownst to the Husnock (and the colonists), one of the inhabitants happened to be an energy being known as a Douwd. The colonists fought and died at the hands of the Husnock and in retaliation, the Douwd destroyed the entire Husnock civilisation, a body-count of some 50 billion lives
KEVIN : No. You don't understand the scope of my crime. I didn't kill just one Husnock, or a hundred, or a thousand -- I killed them all. All! The mothers, the babies, all the Husnock everywhere! (beat) Are eleven thousand people worth fifty billion? Is the love of a woman worth the destruction of an entire species... ?
In the alternate timeline created by the Enteprise-C in TNG: Yesterday's Enterprise, we learn that the Klingon/Federation War has resulted in the deaths of over 40 billion people (hat tip to @hypnosifl for reminding me):
PICARD : Not good enough. Not good enough. I will not ask them to die.
GUINAN : (softly) Forty billion have died in the war...
Moving further down the canon scale, the EU novel Lost Souls focuses on an invasion of the Alpha Quadrant by the Borg. Although their plans are ultimately scuppered, the Federation takes casualties of over sixty-three billion lives lost, spread between the Federation, Romulan Star Empire and Klingon Empire. The conflict also resulted in the destruction of over forty percent of all Starfleet vessels.
Two examples of their obvious combat superiority came shortly after Voyager's initial foray into Borg space. In one engagement, a single 8472 bioship annihilated an entire fleet of 15 vessels with ease, which was the largest grouping of Borg vessels witnessed by a Federation ship up to that point. In a separate battle that occurred in Borg Matrix 010, Grid 19, the Borg lost eight planets, 312 ships, and 4,000,621 drones. The Collective's complete extermination was projected to be only weeks away. (VOY: "Scorpion, Part II")
Species 8472 was the first species to offer "true resistance to the Borg." With their superior biological technology, Species 8472 was able to annihilate large numbers of Borg drones, ships and even planets.
Borg cubes were typically manned by "thousands of drones," and could vary in capacity anywhere from 5,000 to 64,000 to 129,000 drones. (VOY: "Collective", "Unimatrix Zero", "Dark Frontier")
While other conflicts in the Alpha Quadrant incurred massive losses, nothing even came close to the losses the Borg suffered and would have continued to suffer if not for the interaction of Voyager. Without the assistance of Voyager, it is conceivable the Borg would have been completely annihilated.
In one episode it was calculated that the Federation would lose the Dominion War and six hundred billion persons would be killed.
It is hoped that the war actually ended with only a tiny fraction of that number killed, but it still may have been far more than the number of Borg killed by Species 8472.
