Recovery Mode is a built-in recovery loader that the Wii can boot to under certain conditions. It was accessed by Nintendo technicians during the process of factory servicing damaged consoles using a "Waikiki dongle" that was used to then boot the recovery software. Recovery Mode is useful in systems where BootMii or Priiloader are inaccessible and the system is bricked. It also provides useful troubleshooting info as Recovery Mode bypasses the System Menu's WiFi initialization code that causes a brick when the WiFi module is defective or missing. Therefore, when a WiFi brick occurs, Recovery Mode will still boot. Recovery Mode can be used to boot retail software, autoboot discs, or use games with System Menu updates to update the System Menu.
Recovery Mode works when boot1 and boot2 are intact, and the System Menu IOS is not a stub or corrupt. Should any of those 3 components be compromised, Recovery Mode will not boot and the system will appear to be Low-level bricked.
Version Differences
On System Menu versions >= 2.1, the version number will be displayed in the corner when Recovery Mode is booted. From here, you can insert an autoboot disc or a game with a system update that's greater than the version installed. In order to boot retail games, a drivechip is required or the Priiloader patch that allows Recovery Mode to boot any game is enabled. However, any brick that doesn't break Priiloader can be fixed with Priiloader, so Recovery Mode will be useless there. Despite this, Recovery mode is still used in cases where a Korean Wii is updated to System Menu 4.2 or higher and Priiloader is overwritten. The Wii will be bricked with Error 003 and a drivechip will be required to recover the system.
On System Menus before 2.1, Recovery Mode will not display a version number and only autoboot discs will work. An autoboot disc is any disc which ID starts with 0 or 1. There are no retail games that start with 0 or 1, so a drivechip will be required.
Smash Stack
With a drivechip installed, one can boot a copy of Super Smash Bros. Brawl and load the Smash Stack exploit to launch the Hackmii installer or the HBC and use that to load recovery software.
Alternatively, if you already have the save exploits installed, you can use something else like the Twilight Hack or another savegame exploit to load recovery software, but Smash Stack is convenient for working off the SD card.
Recovery Software
For System Menu related bricks, like those caused by region changing, Multi Mod Manager or some other WAD Manager is useful for changing regions or potentially reinstalling the system menu. It can also be used for uninstalling WADs causing Banner Bricks.
For Error 003, KoreanKii should be used to remove the Korean Wii's region-specific encryption key that causes the brick. Alternatively, System Menu 4.1 can be installed instead with a WAD manager using NUS.
For WiFi Bricks, simply having recovery mode booting is an indicator that everything up to the System Menu IOS is functional and that the WiFi module is the more likely cause of a dead Wii.
BootMii can be used to restore a NAND backup as a last resort.
With SysCheck, you can get a list of all (c)IOSes installed and other information useful for diagnostic purposes.
The Priiloader Installer could be useful for restoring a Priiloader that was overwritten by a System Menu update.
If the HBC or BootMii was suspected to have been overwritten by an update, or some other procedure, then upon loading into the Hackmii Installer, you can simply reinstall them no problem.
csm-installer is the only homebrew that should be used for installing themes, as it prevents the installation of themes that can cause a brick.
SaveMii Dongle
If you're able to get your hands on one, the SaveMii Recovery Dongle can be inserted into the Wii's GC memory card slot and will boot Recovery Mode without needing a GC controller. The SaveMii dongle has existed for years but it is completely unnecessary with SaveMiiFrii. It was created by fail0verflow, formally known as Team Twiizers.
SaveMiiFrii
With a GC controller plugged into Slot 4, you can hold down all 4 DPAD buttons then power on the Wii to access Recovery Mode. The best way to do so is by disassembling the controller and using the DPAD's membrane to hold down all 4 buttons, as it's extremely difficult to hold all 4 buttons down at once when the controller is fully assembled.