An app that saves you a huge amount of battery by hibernating the apps that you selected. You can use this app without root but it will work a lot better with. There's also a paid key that unlocks experimental features.
A new and innovative keyboard that is lots of smaller and smarter than others. You can switch between a big keyboard and a small keyboard in just a swype. The small keyboard offers a very smart prediction while the big one is just a normal keyboard...
Trigger, the most simple yet feature-full app especially when your phone/tablet has NFC. It can run tasks like Tasker but it is far more simple to use and has awesome NFC compatibility. Buy some tags and you're good to go!
One of the best apps if you're into making your phone completely run tasks automatically that you've told it to do. The things you can do with this app are endless. There are also a lot of tutorials online.
An awesome solution to your backup needings. This app can backup your data or your apps with data included to your SD-Card, Internal memory and services like Google Drive. This app is for non-root users too, tough root users will have more options.