In Deep Space Nine, we see the
largest fleets assembled in Star Trek. Large deployments of hundreds to
several thousand ships were common in the Dominion War; typical urgent
missions involved dozens of warships.

It is
possible for small resourceful factions within any major power to
construct dozens of ships in secret within a couple years' time.
The Klingons' battlefleet numbered several thousand warships, declining
significantly in the latter phases of the Dominion War. By late in the
final year of the war, the Klingon Empire still had at least 1500
warships conducting offensive operations, while the Alpha Quadrant
Dominion (Breen, Jem'Hadar, and Cardassians) had 30,000 warships
between them.

The
Cardassians themselves were facing defeat from one third of the Klingon
fleet; given that the
Galor
class making up the backbone of the Cardassian fleet is not too much
weaker than the typical Klingon warship, it is likely that the
Cardassian fleet after the Federation war was 1/3-1/2 the size of the
Klingon fleet.
The Klingon-Romulan-Federation alliance operated many thousands of
warships, deployed in joint fleets numbering 100-400 ships. The number
of vessels per fleet appears to have increased over time thanks to
increased Romulan support of the war, with thousands of ships
apparently
lost on both sides. The Allies may have had as many as 15,000 warships
overall.

In
"Defiant," we see 26 Cardassian
warships searching for the Defiant; they plus 15 outposts report no
sign of the Defiant within a half hour's time. Once it is found, ten
warships box it in behind from 6 light years away, while five Obsidian
Order ships lie ahead of it.
Twenty ships attack the Founder's homeworld in
"The Die is Cast," intending to
wipe it out. They are ambushed by a somewhat larger force.
In another high-pressure raid, the Klingons attack Trelka V with five
birds of prey in
"Once More Unto
the Breach."
"The Way of the Warrior"
- the first wave of the Klingon assault, striking from DS9, has
"well over one hundred ships"
in it. At least thirty warships will be stationed around Ty'Gykor at
any
given time in
"Apocalypse Rising."
"In Purgatory's Shadow"
a fleet of
"fifty or more"
Jem'Hadar warships is on their way through the wormhole.

There
"could be fifty" ships
constructed in Orias in secret by the Obsidian Order in
"Defiant." Roughly twenty
actually show up in
"The Die is
Cast," in which the Obsidian Order and Tal Shiar launch an
attack on the Founders' homeworld.
"The Way of the Warrior" - the
Klingon Empire attacks the Cardassian Empire with a total of roughly
one third of their fleet, which includes somewhere over one hundred
warships. How much more is unclear without reference to other
materials.
"When it Rains" - there will be
1500 Klingon warships modified to the new reactor standards
within a few days. These will be outnumbered 20:1 by the Dominion
fleet, which is therefore 30,000 strong. 50 ships lost along with a set
of spacedocks is considered a high price for the Dominion taking DS9,
however.

Seventh
Fleet had 112 ships before engaging the Jem'Hadar in
"Time to Stand," and only 14
afterwards, a figure also confirmed in
"Inquisition."
In
"When it Rains," the
fleet at Chin'Toka numbered 312.
In the battle to retake DS9 in
"Sacrifice
of Angels," "thousands"
of waiting Jem'Hadar ships (2800) sit on the other side of the
wormhole,
waiting to reinforce the Cardassians. The Dominion fleet defending the
wormhole (1254) outnumbers the Federation ships engaging it (609
vessels, 60% assembled) by 2:1. Given that the Federation fleet was
losing until the Klingons showed up. The balance of force was close to
even once the Romulans joined the alliance; this suggests a total fleet
of around 15,000 warships for the three powers.
At
least 11 ships dropped out en route, giving us a ~2% mission abort rate
for the battered fleet.
"The Dogs of War" -
a
fresh offensive against the Dominion would cost
"thousands of ships."
The allies therefore have multiple thousands of warships remaining. The
Cardassian rebellion in
"What You
Leave Behind" plans to cut the Dominion fleet off from ground
support, leading to its defeat.