Hehe - what a delightful question!
OK, for starters, the average man (let's peg him at 70kg) has about 5 litres, or about 10 pints, of blood. We've covered that question here.
The next figure we need is how much blood the average mosquito sucks from you per bite. Having specialised in the more parochial field of human medicine, I was forced to look that one up. As it turns out, those blood-sucking females (males don't partake) are at least considerate to my poor powers of mathematics, for they suck roughly 5 millionths of a litre (0.000005 litres).
So, by means of a simple division that even I can do in my head, we come up with the figure of one million. One million mosquitos...
(That is, of couse, if they attack all at once. God only knows what the figure would be if you have to start factoring in when they bite, if you have enough time to 'regenerate' that blood in that time, the swelling that accompanies each bite, etc...)