The absolute best launcher you can possibly have on your phone. If you only buy 1 app in this list, this should be that app. Features, development, look...it's the perfect launcher. Covers are an amazing feature.
Twilight is the f.lux for your phone. It adds an overlay filter to your screen, and as the day progresses, it will filter out a customizable amount of the frequency of blue light that keeps you awake at night.
The perfect app to automate every aspect of your phone. If you haven't heard of Tasker, it's too difficult to explain in this description, but anyone will tell you it's worth more than what you'll pay for it.
If any of the "speed up your phone" apps haven't 100% improved your phone, this is the app you need. Cleans up your phone's cache, residual files (files left after uninstalling an app), and any large files/empty folders on your phone.
After Catch (R.I.P.) shut down, this is the only notes app I find comparable. Let's your create #tags in a similar way to Catch noes, syncs with your Google account, has a web interface, and is gorgeous and simple.
The only way to describe this app is the only app management tool you'll ever need. Freeze system bloat so it doesn't bog down your phone, set filters and schedules to automatically back up your apps, upload them to the cloud, and restore them later.