Not so long ago, we simplify registration process at our site leaving only the username field...
As a consequence, we are faced with a problem of creating multiple accounts by the same user and abusing faucet (faucet at our site - 0.007 mBTC and only request every 3 hours when balance is zero).
Guys, what solutions do you recommend?

Thank you!
First thing, claimed faucet each in 3 hours is really suck. It really took so long time before we can claim for the second or third, wonder who are those guy who still want abusing this. There is a good way to how to eliminate them beside banning IP, VPN, or their alt account. The way is, just set high min withdraw and tip and you should be fine from those abuser. Just like Primedice doing now, they have increased min withdraw to 0.004 btc to prevent from faucet abuser.
The abusers wont care about the time limit of the faucet as they could claim it every minute if they create multiple accounts. The only thing that attract people to abuse the faucet is of course the amount of the faucet and their assumption that they can make a living from faucet.