Dolphin is a Gamecube emulator. It also has preliminary support for Wii and basic Triforce emulation (this is pending a commit, and does not run games yet).
Gamecube compatibility is about the same (or worse, due to various core changes and lack of subsequent compatibility work) as previous releases.
Wii compatibility is very low. Some games show their intro movies, that's it. There is preliminary Wiimote emulation but it does not work yet.
We haven't worked on Dolphin for a long time, except for a short burst adding the basic Wii support, and we don't think we will finish it, so we hereby release it, in its current unfinished state, to the world. That's not to say that we won't do any more work on it though. But we really would like to see some new coders join.