This app belongs to "must have" apps. It provides many Unix tools and the vast majority of apps require the BusyBox. If you're up to do anything with your device, it's a duty to install this app.
TitaniumBackup is an universal tool which lets you to freeze applications, fully backup/restore them, move any applications to SD Card and many others. To restore your applications after a data wipe is this app the best.
Another app listed to must have section. Are you about to change your ROM? This is the right app for you. Besides this, the app lets you also manage + backup ROMS, partition your SD-Card, flash the ClockWorkMod Recovery and others.
ROM Toolbox contains just everything in one app. Contains - App Manager, build.prop Editor, Root Explorer, Font Installer, Theme manager, Permission changer, and many, many others.
I guess the must have app for low-end phones is Chainfire. This application lets you play challenging HD games on your weak device like GTA III or GTA Vice City and many others. Unfortunately, the app works only on Froyo/Gingerbread (2.2/2.3).
Set CPU, as you probably expect, lets you overclock/underlock your processor. If you're using custom ROM/Kernel that lets you do this, you can easily overclock your device up to +400Mhz. Use carefully.
Another cool app developed by Chainfire company helps you with your warranty. The app resets your binary count and therefore "gets away" the triangle. (You can see the triangle on boot logo screen). This protection is built on Samsung devices.
Out of your RAM? Is Android "overfilled" with useless applications that steal your free RAM? Not anymore. Greenify is capable to hibernate any app you want, therefore it won't steal your free RAM and your device will be much faster than before.
OTA RootKeeper easily protects your root access across the OTA Updates and restores it back any time you want. That means you don't have to root your device everytime you update your device. Unfortunately, There's no 4.3 support yet.
Your battery may seem a little buggy after flashing a new ROM. It's very recommended to calibrate every time you flash the new ROM.
Did we miss anything? Write down to comments what's your best root-app so we can make another part!