Green Day is an American punk rock band formed in 1987. The graffiti like logo above appeared on their second album Kerplunk.
A similar font for it is Greendays, download it for free here. Green Day logo in a typewriter font, as seen on their fourth album Insomniac. The font used is probably FF Trixie. Green Day logo in a sans serif block text with grunge effects added, as seen on their seventh album American Idiot, probably based on Champion Gothic. Green Day logo in square and dripping text, as seen on 21st Century Breakdown, you can recreate it with a free font named Breakdown, download it for free here. The Green Day logo as seen from the 2012 ¡Uno!, ¡Dos!, ¡Tré! trilogy. As you may have noticed, the font for this logo is the same as the one used in American Idiot and the base font is probably Champion Gothic.