Federation: The registry picture.
The Klingons.
Starship readiness levels and Starfleet's composition.
The balance of power in the Alpha Quadrant - history and subdivisions.
Deployment packets.
Borg and Dominion.

Federation: The Coherent Registry Picture:
There are a number of bedeviling details about the registry numbers. However, if we take the larger picture, it would appear as though it's generally a representation of the UFP fleet as a whole, in a state of roughly exponential growth. There are certain gaps in the registry program, some strange quirks, etc - however, the registries suggest that Starfleet had a few hundred starships in the TOS era, and about 20,000 on duty in the TNG era.

It would appear as though a major surge in production occurred between 2345-2360.

The Klingons:
Taken together, TNG and DS9 suggest that the Klingon Empire fields 1500-5000 active warships in the late 24th century, primarily due to the restrictions of the Dominion War. The Klingon Civil War supports this range firmly, however.

The Klingon fleet has not been expanding swiftly. A heavily militarized society, the Klingon Empire supports a strong fleet, but apparently cannot afford to expand its infrastructure at the same rate as the Federation, losing out on fleet expansion during the peaceful 2345-2365 period.

Starship readiness levels and Starfleet's composition:
About 38% of Starfleet's vessels that can be found within Federation space will be laid up for overhauls, upgrades, or repairs at any given time. If an average of 1-2 vessels are being serviced at any given starbase at any particular point in time, this suggests 2600-5200 active Starfleet vessels within Federation territory, 1600-3300 of which are mission-capable.

This figure does not include runabouts and any other small vessels that do not require dedicated starbase time. It is also difficult to figure out how many Starfleet vessels may be found outside Federation territory. Taking these into account, it is possible for the number of Starfleet vessels floating around to approach the 10,000-20,000 range suggested by the registry numbers.

Mission abort rates would appear to be no more than 2% even in the worst of times for active Starfleet vessels. This is low by modern standards.

The balance of power in the Alpha Quadrant - history and subdivisions:
22nd Century:
The Klingons are a dominant power locally, capable of outmuscling most of their neighbors. The Xindi are also a significant regional power.

The Romulans engage in a war with the fledgling Federation, whose military force comes mostly from Vulcan and Andor; they lose, badly. Between them, the Andorians, Vulcans, Tellerites, Rigellians, and Humans can spare over a hundred fighting ships.

2160s-2260s: The Romulans are confined by the superior military force of the Federation.

2260s-2300:
The Federation and Klingon Empire are closely balanced. The Federation appears to have the edge, but only barely. Earth is now the primary military mover in the Federation, in part due to humanity's rapid expansion and the rise of Vulcan pacifism. The Romulan Star Empire leads a three-way arms race with the development of plasma torpedos and cloaking devices; a brief alliance between Romulans and Klingons leads to an exchange of military technologies and ships.

The Xindi are no longer worth mentioning as a military faction. Logically, all three of these major powers have hundreds of starships, possibly as much as a thousand, under their command.

2340s:
The Klingon Empire is at the height of its military powers. In spite of hostile relations with the Romulan Empire, the Klingon fleet is position to start a long but victorious war against the Federation.

Instead, peace breaks out with all parties, and Starfleet takes this opportunity to go on a building spree, checked only by the onset of war with the Cardassians.

2360s:
The Klingon Empire has declined in power relative to the Federation, which now holds a clearly superior position as it concludes a conflict with the Cardassians. The Ferengi Association is considered a clear rival to the Federation. The Romulan fleet is also considered a significant threat to the Federation; an assortment of major and minor powers remain uninvolved.

A single Borg vessel is a dramatic threat to the Federation. It is clear that the Borg are considered to be in a superior position of power in the galaxy.

2370s:
After the conclusion of their civil war, the Klingons still have a powerful enough fleet to defeat the Cardassians easily. A tripartate alliance between Jem'Hadar deployed to the Alpha Quadrant, the remaining Cardassian fleet, and the Breen is roughly equal in power to the Federation, Klingon, and Romulan fleets in a three year long war.

An assortment of both major and minor powers remain uninvolved.

Deployment Packets:
Taken as a whole, fleet deployment habits are fairly consistent:

• 1-3 starships are typically deployed for normal situations or as tactical working groups.
• An emergency deployment will number in the dozens.
• Major fleets in wartime will number in the hundreds.

The Borg and Dominion:
The true power of the Dominion is difficult to gauge. What is known is that the Gamma Quadrant Dominion has a greater force than the Alpha Quadrant Dominion's 30,000 warships; how much greater is unclear. It could be anywhere from twice the size to ten times the size.

The Borg, however, are known, albeit not particularly well. The average Borg vessel has a crew of roughly ten thousand, and is no less than a match for the typical front-line warship of any Alpha Quadrant power individually. Multiplying by the millions of vessels the Borg have, and it is clear that the Borg have a fleet hundreds of times stronger than any Alpha Quadrant power.

Both of these powers are considered to have a total fleet that is overwhelming compared to any of the above.