As you an see from my signature, I like to have full control over what I own. Here I will list all the root apps/tweaks that I'm using: Android Lollipop: AdAway, AFWall+, App Ops, BusyBox Free, Clean Master, Greenify, Llama, Lucky Patcher, SD Maid, X-plore. iOS 8.1: AppInfo, AppSync, iAppLock, iCleaner Pro, iFile, Light Untrusted Hosts Blocker, LocalIAPStore, PasswordPilot, ShowCase, SwipeSelection, WiFi Passwords. Chrome OS Beta: crouton, dev_install, qemacs, xset (dpms force off) Feel free to post your experiences here.
Oh yeah, did I miss any gems exclusively in F-Droid? I had Autostarts, but Clean Master pretty much replaced it although neither successfully manages startup/background in Lollipop... *Found oandbackup but just noticed Lucky Patcher can backup and block ads via HOSTS. No need for AdAway or F-Droid then.
Revised list for Android 5.0.1: AFWall+, App Ops, BusyBox Free, Clean Master, Dashboard, Greenify, Keep for Pebble, Llama, Lucky Patcher, Sixaxis Controller, SD Maid, StickMount, X-plore iOS 8.1.2: AppInfo, AppSync, Controllers For All, iAppLock, iCleaner Pro, iFile, Experimental Untrusted Hosts Blocker, LocalIAPStore, Nitrous, ShowCase, SwipeSelection, WiFi Passwords