Don't worry, F-Droid is an open source app store and all the apps inside are only shown if they are open source as well. This app store is not a pirate market like so many other alternative app stores. Well, they done it again. 
AdAway, Adfree, etc. have all been pulled for violating Play Store guidelines. I myself dislike this. I prefer to donate to projects and websites and contribute instead of viewing ads. I buy the pro version of an app whenever possible, but some apps like Angry birds (although I never play it) and The Weather Channel have no way to remove ads. I'm all for helping developers and such (I contribute around here, and may get a Premium membership in the future) and always pay to remove ads if there is an option to, but now it has became more difficult. But I have a geeky way of sidestepping this. 
Search for F-Droid. It's an app store with only free software that would never pull an app unless it had malware or done something crazy like steal personal info, like most apps on the Play Store. You can still use the Play Store with this installed. Be aware that it's a little slow on my end. So I will provide links for F-Droid and the latest version of AdAway from yours truly's Nexus 4. Give me a sec here guys! Remember, just because you don't like ads is no excuse for not contributing. Help here around AF as much as possible, buy premium, help the mods, become a guide, and that should make up for any ad income missed. Nothing personal here, AF ads are safe, but so many sites ads have given me malware on my PC. If anyone has the ad servers from here, I will gladly include some instructions to whitelist them in AdAway. I trust AF, but sites can get hacked, some sites use sketchy ad providers, etc. Remember that if AF needs any help, I'm always here for you guys. 
AdAway v2.8.1 APK:
https://www.dropbox.com/s/b3lyvq3vor25m2m/org.adaway_48.apk
Direct Link of v2.8.1 from F-Droid:
https://f-droid.org/repo/org.adaway_48.apk
Special AdAway (May or may not work on KitKat):
https://www.dropbox.com/s/q6gq5binm2wbrqf/org.adaway-v47-workaroundbuild2.apk
F-Droid v0.63 APK:
https://www.dropbox.com/s/935t0dsrtpuwtd1/org.fdroid.fdroid_630.apk
Direct link of v0.63 APK from F-Droid:
https://f-droid.org/repo/org.fdroid.fdroid_630.apk
UPDATE:
I have included two links to the updated version of F-Droid. It is smoother, noticeably faster, and you can now swipe left of right to switch tabs in the UI. I also included a new RSS Reader that is free, open source, holo designed, and works WITHOUT any online service! This is a relatively new app, and it is also available on Google Play. FeedEx is the app. It may just be the Google Reader replacement for you. Note that it requires an ICS based ROM or better (4.0.3 and up to be exact). I would recommend BSydz Paranoid Android based off ICS for this one. The app appears to be only a month old as of the original time I wrote this thread. It's a fork of SparseRSS. UPDATE: I highly recommend this app even on a new Nexus 5 with KitKat. It's been only a few weeks since KitKat came out, and it's already optimized for it. You can theme it to be back in preferences, share to the app from your favorite browser, view feeds in a web view, import and export feeds (this also uses the new KitKat file chooser thingy if you have KitKat), it has a navigation drawer, comes with widgets, doesn't force you to use the cloud, and is open source to the point of being practically RMS-approved in theory under the GPLv3. And did I mention it's free (as in beer) as well? Better than Feedly for me.
FeedEx v1.5.4 APK:
https://www.dropbox.com/s/kmquj2fffvqhryv/net.fred.feedex_40.apk
Direct link of FeedEx v1.5.4 APK from F-Droid:
https://f-droid.org/repo/net.fred.feedex_40.apk
Direct link of FeedEx v1.5.4 APK from Google Play:
https://play.google.com/store/apps/details?id=net.fred.feedex
Leave comments if you have anything to say. Or if you find any other good software on F-Droid.
Anyhow, about that special AdAway build. It's meant for KitKat. I got someone I know to do some special workarounds to get version 2.8 working flawlessly for me on KitKat. It's not perfect, but it works. He done this as a good favor for me, and he published the code for the original developer on GitHub. AdAway would hang for me on KitKat, but this special build includes a workaround, albeit not a clean patch, fixes the issue. Just another reason to keep checking back here even if you're on KitKat and haven't touched a Triumph in years.
AdAway, Adfree, etc. have all been pulled for violating Play Store guidelines. I myself dislike this. I prefer to donate to projects and websites and contribute instead of viewing ads. I buy the pro version of an app whenever possible, but some apps like Angry birds (although I never play it) and The Weather Channel have no way to remove ads. I'm all for helping developers and such (I contribute around here, and may get a Premium membership in the future) and always pay to remove ads if there is an option to, but now it has became more difficult. But I have a geeky way of sidestepping this. Search for F-Droid. It's an app store with only free software that would never pull an app unless it had malware or done something crazy like steal personal info, like most apps on the Play Store. You can still use the Play Store with this installed. Be aware that it's a little slow on my end. So I will provide links for F-Droid and the latest version of AdAway from yours truly's Nexus 4. Give me a sec here guys! Remember, just because you don't like ads is no excuse for not contributing. Help here around AF as much as possible, buy premium, help the mods, become a guide, and that should make up for any ad income missed. Nothing personal here, AF ads are safe, but so many sites ads have given me malware on my PC. If anyone has the ad servers from here, I will gladly include some instructions to whitelist them in AdAway. I trust AF, but sites can get hacked, some sites use sketchy ad providers, etc. Remember that if AF needs any help, I'm always here for you guys. AdAway v2.8.1 APK:
https://www.dropbox.com/s/b3lyvq3vor25m2m/org.adaway_48.apk
Direct Link of v2.8.1 from F-Droid:
https://f-droid.org/repo/org.adaway_48.apk
Special AdAway (May or may not work on KitKat):
https://www.dropbox.com/s/q6gq5binm2wbrqf/org.adaway-v47-workaroundbuild2.apk
F-Droid v0.63 APK:
https://www.dropbox.com/s/935t0dsrtpuwtd1/org.fdroid.fdroid_630.apk
Direct link of v0.63 APK from F-Droid:
https://f-droid.org/repo/org.fdroid.fdroid_630.apk
UPDATE:
I have included two links to the updated version of F-Droid. It is smoother, noticeably faster, and you can now swipe left of right to switch tabs in the UI. I also included a new RSS Reader that is free, open source, holo designed, and works WITHOUT any online service! This is a relatively new app, and it is also available on Google Play. FeedEx is the app. It may just be the Google Reader replacement for you. Note that it requires an ICS based ROM or better (4.0.3 and up to be exact). I would recommend BSydz Paranoid Android based off ICS for this one. The app appears to be only a month old as of the original time I wrote this thread. It's a fork of SparseRSS. UPDATE: I highly recommend this app even on a new Nexus 5 with KitKat. It's been only a few weeks since KitKat came out, and it's already optimized for it. You can theme it to be back in preferences, share to the app from your favorite browser, view feeds in a web view, import and export feeds (this also uses the new KitKat file chooser thingy if you have KitKat), it has a navigation drawer, comes with widgets, doesn't force you to use the cloud, and is open source to the point of being practically RMS-approved in theory under the GPLv3. And did I mention it's free (as in beer) as well? Better than Feedly for me.
FeedEx v1.5.4 APK:
https://www.dropbox.com/s/kmquj2fffvqhryv/net.fred.feedex_40.apk
Direct link of FeedEx v1.5.4 APK from F-Droid:
https://f-droid.org/repo/net.fred.feedex_40.apk
Direct link of FeedEx v1.5.4 APK from Google Play:
https://play.google.com/store/apps/details?id=net.fred.feedex
Leave comments if you have anything to say. Or if you find any other good software on F-Droid.
Anyhow, about that special AdAway build. It's meant for KitKat. I got someone I know to do some special workarounds to get version 2.8 working flawlessly for me on KitKat. It's not perfect, but it works. He done this as a good favor for me, and he published the code for the original developer on GitHub. AdAway would hang for me on KitKat, but this special build includes a workaround, albeit not a clean patch, fixes the issue. Just another reason to keep checking back here even if you're on KitKat and haven't touched a Triumph in years.
