Yes, Gnarls Barkley orginally sung the song, it was his song.
However many other artists have covered Gnarls Barkleys song; The Kooks, Nelly Furtado, and The Zutons have covered "Crazy" on BBC Radio 1's Live Lounge. Folk singer Ray LaMontagne has also covered the song and Paris Hilton had delayed the release of her debut album Paris to include a cover of "Crazy" as well, although it was not included in the final track list. Other artists, including The Raconteurs, Billy Idol, The Academy Is... (with Schleprok of Gym Class Heroes), and Texas have performed cover versions of the song live in concert.
I hope this helps!