I've found a few interesting ways to get some coins for free.
They're called faucets, you basically just have to log on and claim the coins every so often. Seems like they make money off ads, so the coins are a way of getting page clicks. You'll need to make a CoinPot account (hot wallet), but after that you should be set. Tip: I would suggest using the "solve media" captcha verification over over the recaptcha, as the latter tends to loop on occation, causing it to take an obnoxiously long time to actually verify (i've gone through 8 recaptchas on a single claim occasionally)
http://moonliteco.in/?ref=15071ef26a56
http://moondash.co.in/?ref=EF881F3574D4
http://moondoge.co.in/?ref=9dbaffecf1ac
http://moonbit.co.in/?ref=06ddbfb47389
http://moonb.ch/?ref=2FD89D946EA3
http://freedoge.co.in/?r=1746292
https://freebitco.in/?r=11465076
http://bonusbitcoin.co/?ref=1FFAB7B3EF74
This one, called "Qoinpro", just requires registration and then accumulates the coins automatically and allows you to get in on some airdrops: https://qoinpro.com/886a438836011c2de4cc1fc6f5ec3b38
As a tip: these wallets tend to have fees/minimums for withdraw for certain coins, but due to DOGE coin's relative low cost per coin, the fees are normally low. After about a week I converted the coins i got on CoinPot to DOGE and transferred them to my (offline) wallet with no fees. Got 142.35DOGE. Not a ton (~$1.50 worth), but it's decent for a little time-killer which requires no monetary input.
I will post more lists as I find sites that are actually worth the time input, so remember to follow and vote. I've found a lot more, but many were just too over-loaded with ads that made it too frustrating to be worth it, in my opinion, unlike those listed above.