Green Day - Insomniac (best green day album lyrically. They were also my favorite band when i was 13 so i had to put them on here somewhere) https://www.youtube.com/watch?v=MNiYrKyERv0
The Steinways - Missed The Boat (this album was a huge influence on my own songwriting. They sound like the stuff i write if it wasn't acoustic) https://www.youtube.com/watch?v=edNJPHwqKys
Piglet - Lava Land (This is my favorite math rock record. Its very melodic and doesn't try too hard to show you how technical they can be. Its one of the few math rock records I believe almost anyone can appreciate even if they don't like complicated music)
https://www.youtube.com/watch?v=tKNPUH8UEO8
Paul Baribeau - ST (beautifully personal folk punk) https://www.youtube.com/watch?v=15g2LQXmouU
AFI - Black Sails In the Sunset (New AFI stuff makes my ears bleed but I have to admit to loving this album. It has a lot of variety in terms of tempo and aggression and the lyrics do a good job at being dark and poetic while only rarely seeming like they're trying too hard. Davey's vocals were also pretty sweet before he fucked up his voice.)
https://www.youtube.com/watch?v=d2KohTWbNdk
Descendents - Milo Goes to College. (This was the album that got me into real punk rawk. i think my mom told me to listen to this band.) https://www.youtube.com/watch?v=IpfXVd-zfrg
Melt Banana - Cell Scape (Melt banana is a noise punk band from japan. Their guitarist uses a lot of really fucking crazy effects and their vocalist sounds like an anime girl getting fucked in the ass. A lot of their songs are really fast and energetic. https://www.youtube.com/watch?v=cFwCpw8AQBg