Letterbomb is the latest Wii exploit and is currently the only to way to hack a Wii on System Menu 4.3 without using a game. It's likely that it will not be ported to any lower System Menus since Bannerbomb is available for those.
Letterbomb uses a yet-to-be-specified exploit in the Wii Messageboard.
System Menu 4.3 (E, U, K, J)
(If you already know how to get your Wii's WiFi MAC Address, skip to step 2)
1. Go to your Wii's Settings menu. Select "Internet" on page 2. Select "Console Information". Record your Wii's MAC Address for use in the next step.
2. Follow the link provided above to the HackMii download page.
3. Make sure "Bundle the HackMii Installer for Me" is checked. Select your System Menu region, enter in your Wii's WiFi MAC Address, fill in the captcha, and "cut either wire".
4. Extract the contents of the freshly downloaded .zip file onto the root of your SD card.
5. Insert the SD card into your Wii.
6. Go to your Messageboard (button on bottom-right of Menu) and navigate to "Yesterday" (depending on your timezone, the exploit could show up under "Today").
7. Click on the pink envelope with the bomb to run the HackMii installer.
Additional Hackmii installer steps:
8. You will see a Scam warning screen.
Wait for the message at the bottom to appear, then press 1.
9. You will see a screen like this one:
Depending on your wii, it will show different things behind BootMii:.
Now we get to the main menu, where we can install everything.
First install the Homebrew Channel (choose Yes, continue).
The Homebrew Channel will now be installed on your Wii.
Optional (Recommended) Steps: Installing BootMii
BootMii is a helps greatly with Brick protection and it is recommended to install it.
It is not required however.
These steps don't work on WiiU
10. In the HackMii main menu, choose BootMii... and press A. You will get another menu.
11. Before BootMii will work, we need to prepare our SD card, so do that first with the third option.
12. Install BootMii as IOS. This will always work.
13. If you're one of the lucky winners, choose install Bootmii as Boot2, then Yes, continue and let it install.
Once you're done, return to the Main menu and choose Exit. It will reboot the Wii.
If you installed BootMii as Boot2, the BootMii menu will appear every time.
14. Don't forget to restore your old private folder if you had one!
So, was that it?
It mostly depends on what you want to do. Many Wii applications will already work for you now.
However, if you want more, like backup loading, custom themes, etc; you will need to continue below.