The Dominion War - Over 1 billion
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 - 9 billion
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.
Federation / Husnock skirmish - 50 billion
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... ?
The Klingon/Federation War - 40 billion
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...
The Borg invasion of the Alpha Quadrant - 63 billion
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.