(includes Pro Skater 3)
Uses an exploit with the Create a Skater mode to softmod the Playstation 1
(Thanks Megateixeira!)

Twilight Hack, one of the first ways to enable homebrew on the Wii. Exploits a buffer overflow glitch when saving Epona's name to memory, and can be used to run a custom boot file from the SD card.

For the Wii version of Lego Batman, Bathaxx was a hacked game save which comes strapped with homebrew applications.

Indiana Pwns is a hacked game save for the Wii version of Lego Indiana Jones, which executes homebrew applications from the SD card.

Return of the Jodi is a hacked game save for the Wii version of Lego Star Wars: The Complete Saga, which executes a homebrew application from the SD card.

Eri HaKawai is achieved by playing a hacked game save for the Wii version of Tales of Symphonia: Dawn of the New World which executes a homebrew application from an external SD card.

Smash Stack is an exploit that uses a flaw in the custom stages in Super Smash Bros by using unsigned code from within the SD card.

Yu-Gi-OWNED! is a modified game save that triggers a buffer overflow which activates unsigned code within the SD card.

A Wololo save file exploit that can be used to access a homebrew loader for both the PSP and the Vita.
(Thanks ConsultorIvone!)

Ninjhax, one of the first breakthroughs in 3DS hacking. Uses an ingame QR function to access unsigned code within the SD card.

(Also applies to Omega Sapphire)
Basehaxx is an exploit that uses the loading of secret bases to activate unsigned code.

Genhax, only compatible with the JP version of the game, is a custom save that allows the user to activate unsigned code.

Humblehax, an exploit for the 3DS version of the game.

DoodleBomb was an exploit to access the Homebrew launcher with SwapDoodle, allows you to boot a friend into the Homebrew launcher as well.

Ironhax, another 3DS exploit.

Oot3dhax, a save game exploit.

Smashbroshax, an explout that uses a wifi beacon to run unsigned code.

Steelhax exploits hacked savedata for homebrew.

V*hax, a hacked save exploit for the 3DS version of the game.

Freakyhax, a QR code exploit to run unsigned code from the SD card.
(Thanks Guttertrash!)

Has a save exploit compatible with the PS2, Wii, Gamecube, and Xbox.
(Thanks Jamesbuc!)

Haxchi exploit to use DSiware to install homebrew onto the WiiU.
Quite a few of these, in the interest of not clogging up the list with the same exploit, the games this works with are all here http://wiiubru.com/go/haxchititles/index.html
(Thanks Midrulean!)