darkwing_duck1
Vice Admiral
Ron Moore once said he figured there were between five and eight thousand ships in the Starfleet, and while he was not usually the go-to guy for this sort of thing (...[TECH]), this feels right to me.
This number would not include certain kinds of ships (science ships, freighters, etc.) that might receive numbers in the registry scheme but are not Starfleet ships of the line. That leaves us plenty of wiggle room.
I think the number should be kept relatively low, because the ships seem to operate independently so often and I really can believe Starfleet is spread somewhat thin sooner than I can believe the opposite, because it seems to have taken some significant time to assemble fleets, and because the loss of 40 at Wolf 359 was evidently significant. I think maybe seven or eight thousand ships before the Dominion War and perhaps somewhat fewer afterward feels right.
Picard once said the Federation was spread out "over a thousand light years".
He said "eight thousand light years," and since this really gets hard to think about, that's got to be like two "pseudopods" or separated "enclaves" of Federated worlds that are really far away from one another. The Federation "inner perimeter" seems to be only a couple of hundred light years across.
Either way, that's a heck of a lot of cubic light years of volume to cover. At Warp 5 it takes a ship a nominal month to cover 20 ly (barring a fortutous "warp highway").
One firm datapoint we have is that at the height of the war, the dominion was fielding over 20,000 ships. The Klingons at that point had an effective fighting force of ~1500 ships. Make of that what you will...