Do we have knowledge on the number of vessels in the armadas of the various belligerents of the Napoleonic wars? Information on the types of boats, captured vessels, and sunk vessels will also be nice.
I can tell you two things, how many were under Nelson's fleet in the Mediterranean and how many were in commission throughout the world in May 1804.
Under Nelson's command were 13 Ships of the Line, 1 Fifty, 11 Frigates, 10 Sloops, 3 Bombs, 6 Gunboats and 2 Cutter and Schooners.
In total commission (throughout the world) were 88 Ships of the Line, 13 Fifties, 125 Frigates, 92 Sloops, 18 Bombs, 40 Gunbrigs, 6 Gunboats and 82 Cutter and Schooners and 41 Armed ships.
Source: The Command of the Ocean, A Naval History of Britain, 1649–1815, N.A.M Rodger.
According to www.napolun.com the European fleet strengths, in terms of Ships of the Line (1st to 3rd rates), in 1808-1809 (shortly after Trafalgar) were:
Also according to that website, in 1805 the Great Britain (presumably including state owned trade ships etc) had a total fleet size of approaching 950 vessels.
The website has a list of sources at the bottom of the page for further reading.