Modest Mouse, "So Much Beauty In Dirt"
This comes from the 2001 EP Everywhere and His Nasty Parlor Tricks, which in turn pulls a few songs from an earlier EP and adds a few new ones. This is from the peak Modest Mouse period, from their three album run from The Lonesome Crowded West through Good News for People Who Love Bad News, so it's good stuff.
Mudhoney, "Here Comes Sickness"
If there's one album I'd point to that defines grunge to me, it's not Nirvana's Nevermind. Sure, that's the commercial breakthrough, but I'd instead point at Mudhoney's first, self-titled record as really being the heart of grunge. It marries the energy of punk and the power of metal, with a certain grime that really sets the genre off. This is basically the sound that so many bands were chasing in their own way before grunge got huge and changed into sour grunting.
False, "The Deluge"
Can I talk about how annoying it is when bands have multiple albums named the same thing? It's super annoying! And False goes another step by just going ahead and having two untitled albums. Fantastic work! Thanks, False!
Skavoovie & The Epitones, "She Sure Can Cook"
The third-wave of ska featured a lot of ska punk, which is mostly what people remember. But there were bands that went much further into the horns, and few of them went as far as Skavoovie & The Epitones. They cheerfully stretched across a bunch of genres beyond just ska, mixing in big band, jazz, and yes, some ska punk. It's a fun mix of stuff, and as long as you're not allergic to the vocal interjections here, they're worth checking out.
Samiam, "Well"
I think every punk fan has a few albums that they just love more than everybody else. For me, one of those records is Samiam's Billy, a record that doesn't particularly stand out in any way, but hit me at the right age and in the right mood so that it's always stuck with me.