UPD. Well, it happens... After several days, today I suspect that the below four projects are a scam. Personally, I will keep going with them for a while to become quite sure of it, but I want everyone to be warned, better late than never.
Most crypto-faucets are not "accumulating". I mean, usually, you click through banners, get your 1 satoshi and go to cool down for, say, an hour. When you come back after that hour, you get the same 1 satoshi again. If you come back after 3 hours instead -- you get the same 1 satoshi, not 3. If you're back over the weekend -- you still get the same 1 satoshi... I hope you got the idea.
Today I'd like to present somehow unique gang of "accumulating" faucets:
- Tfbitcoin.com (BTC)
- Ripplefree.info (XRP)
- Dogecoinfree.info (DOGE)
- Litecoinfree.info (LTC)
- Ethereumfree.info (ETH)
What is so unique about them? They accumulate claims over time. If we take the above example again -- by "accumulating" I mean that you get 3 satoshi if you come in 3 hours, and 24 sats if you come in a day.
Of course, the real accumulating rules of the faucets are not so straightforward:

If you do the math you'll see that claiming every 5 minutes is much more profitable than one claim daily. But anyway, this system can save you at least some honey if for whatever reason you're late from your cool-down leave.
Personally I like those five because of their convenience -- usually I come to collect my honey only once a day.
Disclaimer: I'm not an employee or owner of any faucet or crypto-exchange, including the above-mentioned ones. This article is informational, and not financial advice or an endorsement or guarantee of any kind. I myself have assets at the above-mentioned faucets.