This is a common question by those who have just rooted their phones. What apps, ROMs, benefits, etc. do I get from rooting? What should I be doing now?
You can remount your
/system/ directory read-write, which will allow you to remove carrier-shipped applications you don't like and so on. Root file explorers can allow you to view all folders on your phone, such as
/data/ which is normally protected.
With root access you can patch other apps to gain special access to functions, or removal of self-protection for some apps.
Access to /system also means you can move apps or updates to system apps from /data to /system (with caution!), if the partition has enough space.
Note that moving apps to the sdcard has risks and cons, and should be undertaken only if space is needed. Most modern devices have enough memory for many apps (16GB+), providing that photos/videos/music are stored on an external sdcard.
Some devices already have Wi-Fi tethering out-of-the-box, like the Samsung Galaxy S, so this isn't such a big deal on them unless the carrier charges for the feature.
root is needed for screenshots before 4.0-Ice Cream Sandwich. Most pre-lollipop screen recorders also require root.
There are also many apps that claim to make a full nandroid backup.
AdFree - Removes ads by changing the hosts file (so both ads in apps and in browser)
Adaway - Also blocks in-app adds.
Droid Wall - Firewall application. Got an app that's using up all your data when you're not even using it? Block it with this!
Orbot - Tor app
Cache Mate - Clear cache of all apps
Droid VNC Server - Connect to your phone via VNC
LBE Security Master - Selectively revoke permissions from app
Button Savior - Helps to add on screen button to compensate a failure of a physical button.
ClockSync - to automatically sync the device's time with few predefined atomic clocks.
The Xposed framework allows apps with advanced tweaking functionality to be installed.
ROEHSOFT RAM-EXPANDER (SWAP) - Use SD card for more RAM.
Memory Swapper Free - support swap file.
Though root is not required for flashing new ROMs, many apps that make it easier do require root.
CyanogenMod is a very popular rom that many people put on their phones. It is also easy to install via the ROM Manager app. First install the Clockwork recovery. Then run a backup before you flash any roms.
Also check out "Where can I find stock or custom ROMs for my device" or the XDA forums for other custom roms. Most devices have a specific "Android Development" sub-forum where ROMs are posted.
Always do a nandroid backup before installing any rom or mod! You may also need to wipe all data and cache from your phone before installing or upgrading a ROM.Custom Kernels
One popular set of kernels is those provided by ChevyNo1. You can also download them via the premium version of the ROM Manager. Make a nandroid (ClockworkMod) backup before using these kernels! You'll also want to get SetCPU to make the most out of these kernels.
Start with the low voltage kernels at the lowest speed and work your way up to the 1.2GHz. If your phone is stable up to the 1.2GHz range, then try some of the ultra low voltage kernels. If you start getting force closes, then switch back to a low voltage kernel.
Basically each phone (of the same phone brand/model) varies by which kernel it can handle due to the manufacturing differences between processors. So I may have a Motorola Droid that can run ultra low voltage kernels and yours may not be able to run them. These phones weren't necessarily designed to run like this.
In few words, rooting an Android system means overcome the limitations that were imposed over it by the manufacturer. People may want that for different reasons, but the main one is freedom. Having a rooted phone means you've got all the control over your device.
The main reason people root phones is to install a custom ROM. Custom ROMs are often known for improvements in performance and exclusive features that are not present on manufacturer ROMs, like installing apps on sdcard or taking screenshots. Custom ROMS can also become a system update alternative for those devices that were abandoned by their manufacturers. You can see a review of popular ROMS, as an example, here.
Rooting Android also allows you to uninstall stock apps that you don't use or don't want, besides those that violates user's privacy (see CarrierIQ). Another main reason for doing that is to gain more space on internal storage.
A rooted device lets you install almost any app that requires root access. Those apps generally aim to do something that would not be possible without that privilege. A lot of useful apps were shown on the previous answer, but you may find a lot more available on Google Play. You can find a list of good apps here.
Google is trying to reduce the need for rooting by improving the permitted system services. Nowadays screenshots, screen recording and tethering typically don't require root.The reasons I can think of to still root:
To move files and apps around without restrictions.
/datapartition to the
/systempartition in order to save space and preserve them from factory resets.
To run programs with more power: