Dolphin
Dolphin is a GameCube and Wii emulator usable on personal computers. As a result of this, both Super Smash Bros. Melee and Super Smash Bros. Brawl are playable with the emulator. As Dolphin is currently the most stable GameCube and Wii emulator available for download, it is currently the most popular option for emulating the two games. Dolphin is named after the development codename of the GameCube, "Dolphin".
Outside of its ease of setup and relative stability, Dolphin has since become popular for its use in tool-assisted superplays, especially with JPleal's Perfect Falcon and Perfect Pichu videos. In addition, the emulator allows for the ability to hack textures in both Melee and Brawl. Dolphin has also been focused on because of its built-in netplay functionality for Melee, Brawl, and Brawl's various mods; more recent builds of Dolphin have notably been able to reduce desynching problems that have previously plagued Dolphin's netplay scene.
According to Dolphin's development team, Melee can run in Dolphin without emulation errors. Brawl, however, requires certain graphical requirements set within Dolphin to properly display the various results screens; in single player modes, the screen focusing on the player's character instead becomes a solid green colour, and in multiplayer modes, the text becomes completely illegible. Barring these graphical flaws, the Dolphin development team has stated that Brawl is fully playable in the emulator.
Project M and other Brawl mods can also be run on Dolphin with appropriate settings, and they can also be played online; the Project M Dev Team notably released a version of the mod optimized for Dolphin, allowing it to potentially run better than Brawl itself on some computers.