The Bitcoin Faucet now shows how many coins it has available to give out (on the left-hand side of the page). The number is only moderately accurate-- donations will take 5 or 10 minutes to show up in the balance.
I also implemented another anti-cheating measure that should make casual cheating a little harder (which I don't want to say too much about because that would make it easy for cheaters to know what to do).
I'm very pleasantly surprised at how well freebitcoins is working so far; thanks again to everybody who tried it out and who donated bitcoins to it!