OK - we have
real info, at last.
http://www.census.gov/prod/ec97/97m3329f.pdf
US Census Bureau
Small Arms Ammunition Manufacturing
1997 Economic Census
Table 6a. Products Statistics: 1997 and 1992
Rimfire rifle~pistol cartridges (30 mm or less, 1.18 in. or less) millions.. ......................... 1997: N/A 1992: 3,000.9
Centerfire rifle cartridges (30 mm or less, 1.18 in. or less) millions.. ......................... 1997: 270.1 1992: 554.0
Centerfire pistols, including cartridges interchangeable between rifles and
pistols (30 mm or less, 1.18 in. or less) millions.. ........................................ 1997: 1,148.7 1992: 875.0
Shotgun shells (30 mm or less, 1.18 in. or less) millions.. ..................................... 1997: 1,018.9 1992: 981.5
Small arms ammunition primers (30 mm or less, 1.18 in. or less) millions.. ................... 1997: 2,221.6 1992: 2,027.8
Of course, 1997 isn't very recent, but there's no indication that production has declined. (That large apparent drop in centerfire rifle-only cartridges is at least partly because of an increase in the number of cartridges for which pistols are available. If one guy makes a pistol that fires .223, all .223 sales are moved from the rifle-only to the rifle-and-pistol category.)
The rimfire category doesn't include counts for 1997, because too large a percentage of their data was dollar-value only. But the dollar-value of rimfire nearly doubled between 1992 and 1997, from $60.5 million to $112 million. It'd not be unreasonable to guess that there were more than five billion rounds of rimfire sold in 1997.
(not counting 22lr's of course 
) 
