Maybe you know the story of Gavin Andresen's 'the Bitcoin Faucet'?
Here's a screenshot courtesy of Way Back Machine - Internet Archive plus that bitcoin address - here is a block explorer analysis.

Back in 2010 Andresen developed a website that literally gave away bitcoin. Just for completing a captcha it gave five (FIVE!) BTC per visitor.
In fact, some visitors for example 'Bitcoin Pizza guy' Laszlo complained it was so small, but of course back in 2010, 2011 bitcoin was basically worthless.
Andresen's motives were entirely altruistic, stating "I want Bitcoin to be successful, so I created this little service to give you a few coins to start with.”
My point is that in 2010, 2011 you could argue visiting Andresen's faucet was a waste of time, the amount of bitcoin obtained worthless etc. Exactly the same arguments you could make today.
Thereafter the original free faucet closed down to be replaced by the ad-driven clicks-for-bits type faucets we know today, they boomed but recently with more focus or on privacy, less opportunity with say Google, they are less prominent and some of the best ones (e.g. the Moon series have closed down).
Nevertheless some of the old faucets still survive and payout.
The Best
Freebitco.in - one of oldest, still going strong, giving away up to $200 in bitcoin every hour. Head over to the free BTC page, enter an email, complete the captcha and hit ‘Roll.’ Go back every hour for a new free roll and earn up to $200, also 2 reward points and 2 lottery tickets with every roll which you can use to win prizes. 50% referrals too!

If you haven't joined you should!
I've received and am receiving payouts from this one!
Daily Freebits - another OG* site, get between 1 - 1,200 satoshi every hour (remember 1 bitcoin is 100 million satoshi), sign up is just a bitcoin address, and you can get a pay out to Faucetpay.io to aggregate your faucet earnings.

Faucetpay.io - sign up for access to literally hundreds of faucet sites. Nice clean website too!


I like the sci-fi flavor website and gamification of Cointiply, 25% referral rate, approaching 1.8 million users

*old gangsta
The Rest
There's Bitcoinker - get up to 100,000 satoshi every five minutes, and Bitcoin Reward - 2,500 satoshi just by signing up and Bitcoin Get - earn bitcoin by taking surveys and completing jobs.
My thoughts
Just visiting by yourself, well you have to be pretty optimistic, pretty bullish on future bitcoin prices (one million USD anyone?) to think that you can make reasonable money but perhaps it is worth a punt, if you have the time and the patience.
If you sign up you can get referrals, which all of the links in this post, of course, are, that increases the potential somewhat.
If you have some way to promote, twitter or FB or Instagram or a website, then you'll have even more potential.
Okay, it doesn't hurt to try, does it?
Good luck!
Thumbnail photo by Walter Randlehoff on Unsplash