Enterprise - around 30-50 i would say composed of the Intrepid, Neptune and Sarajevo types along with a few variants and older ships. My guess is by the height of the Romulan War Earth might have had as many as 75-100 ships in service but around the start of the show 30-50 seems like a good number.
TOS - I would guess there were 300+ in service at the time with the 12 constitution classes being top of the line only behind the possibly-existing dreadnaught class of which there were fewer.
TNG/DS9/VOY - I would say there were around 6000+ in service considering they were losing hundreds of ships in various single engagements yet still had plenty more. At the same time mobilizing a fleet of 600 ships was a significant part of the fleet as noted by Dukat and Starfleet themselves. Many of these were the older Mirandas, Oberths and Excelsiors however limiting the true effectiveness of Starfleet.