bitcoin faucetThis is a partial list of the faucets that helped me earn 0.003+ BTC in roughly two month’s time without referrals!  There were others as well, but they either developed problems that couldn’t be worked around, closed down, or began charging hefty fees to pay out.  Network fees the wallets have to pay have gone up, forcing some faucets to change their minimum cash-out balances.  Needless to say, finding a wallet that can accommodate small deposits and continue earning a decent amount every day initially meant going to XAPO to get a wallet there.
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EDIT Jan 2018:  With Moon, Bonus and Bitfun now aggregating earnings over at coinpot, it now makes sense to have your wallet at freebitco instead so that you earn interest.  Use Xapo as your active wallet instead.
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I refer to this as Faucet Alley, because of the dangers that the advertising companies have created around these faucets.  The owners engage in advertising in order to earn the satoshi that they pay you, so you generally don’t want an ad-blocker running so that they can earn what you will get paid.  But as I said in this blog article here, that opens up a whole can of worms that make this a very dark alley to walk down if you don’t have the necessary flashlights and tools in your backpack.  Most faucets you come across carry with them some aspect of this level of danger.  Are the promises worth the pain? Be sure to read my blog article, then come back here to decide for yourself.

XAPO Faucets:

Field Bitcoin: (The most dangerous in my list so far!  Ensure browser settings prevent requests to install software, turn off redirects. Know how to crash browser in case of respawning pop-unders in new windows, clear cache and temp files before resuming session if this occurs)
Cash out every 5 minutes if you wish to, or leave till you’ve accumulated 100 satoshi including compounding bonuses.  Very reliable.  While similar to Moon Bitcoin, it earns at roughly half the rate.
EDIT Jan 2018:  Eventually stopped using this site due to site behaviour.

BTC4Free.site – a CoinGainGuru Faucet: (Pop-overs into new tabs and pop-unders as well. Turn off redirects in your browser’s settings) Generally reliable.  Had hosting issues for roughly a week at one point, but resumed right where they left off.  Also a great source of information about bitcoin.
Cash out every 100 or so satoshi.  Claim amount varies with BTC volatility.
EDIT Jan 2018:  Stopped using this site when earnings got far too small to be of any use.

BTC4Free.today – another CoinGainGuru Faucet: (Pop-overs into new tabs and pop-unders as well. Turn off redirects in your browser’s settings) Generally reliable.  Had hosting issues for roughly a week at one point, but resumed right where they left off.  Also a great source of information about bitcoin.
Cash out every 100 or so satoshi.  Claim amount varies with BTC volatility.
EDIT Jan 2018:  Stopped using this site when earnings got far too small to be of any use.

BTC Source:  (new tab that opens a new window, turn off redirects in your browser’s settings)
Cash out after earning 300 satoshi.  Occasionally runs out of satoshi but will pay after a day or two.
EDIT Jan 2018:  Stopped using this site when earnings got far too small to be of any use.

XapCom: (pop-overs into new tabs periodically, turn off redirects in your browser’s settings)
Cash out after earning 300 satoshi. Occasionally runs out of satoshi but will pay after a day or two.
EDIT Jan 2018:  Stopped using this site when earnings got far too small to be of any use.

EarnAutoMoney: Discovered this faucet AFTER earning my 0.003+ BTC.  So far it appears safe, which might make it the second safe faucet in this entire list.
Cash out is instant and generally around 50 satoshi, although sometimes 75 or 100.  Site claims up to 1000 every 90 minutes.

Non-XAPO faucets:

Moon Bitcoin: (Pop-overs into new tabs and pop-unders as well. Turn off redirects in your browser’s settings)
Connected to coinpot for collection of earnings.  Withdraw from Coinpot whenever you wish.

Bonus Bitcoin: (Pop-overs and pop-unders occasionally, ensure browser redirects are turned off, sometimes has trouble connecting to reCaptcha)
Connected to coinpot for collection of earnings.  Withdraw from Coinpot whenever you wish.

Freebitco.in: (very few ads, recaptcha doesn’t always work, switch to solvemedia to carry on)
Cash out after earning at least 30,000 satoshi.  Now offering 4.08% annual interest earned daily on amounts over 30,000 satoshi, effectively creating a savings account for BTC.

Bitfun:  (Pop-over and unders occasionally, ensure browser redirects are turned off) Connected to coinpot for collection of earnings.  Withdraw from Coinpot whenever you wish.

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It should be noted that as of July 2017, the remaining active faucets due to changes on their end, became Moonbit, Bonus Bitcoin, Freebitco.in, and Bitfun.

Also, due to persistent issues with Google’s Recaptcha, many of these sites now offer captcha alternatives that are much easier and less frustrating to use.
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Non-Faucet Earning Sites:

Search Trade: Earn a bit of satoshi every time you do a search (up to 40 paid searches per day).  Pick from your choice of search engines such as Google and Bing.  Cash out after reaching 10,000 satoshi or more. Good for search terms not requiring time/date/continent filters.

BTC Clicks:  Earn satoshi for clicking on ads.  This site has paid me at least FOUR times (as of Feb 2018) since early August 2017.

Coinbulb:  Earn satoshi for clicking on ads.  Has now paid me for the first time (April 2017) since September 2017.  Satoshi earnings are higher than BTCClicks, but fewer ads, so it takes longer doing it without referrals.

adBTC: Earn satoshi for clicking on ads.  Just joined as of January 2018.

Bitter.io: Earn satoshi for clicking on ads. Just joined as of January 2018. Requires Chrome extension. Can work in Opera with “Install Chrome Extensions” plugin installed first.