Considering my scene is more popular than Catie's (I have Death Cab, Modest Mouse, The Shins, etc.) I'm going to focus on obscure side projects when it comes to famous musicians and then just generally unheard of bands.
Heatmiser
Heatmiser was Elliott Smith/Neil Gust's mutual project when at college but the band later relocated to Portland where they formed the line up we all don't know of today. Which would later be reconfigured to include Sam Coomes and on their final tour John Moen on drums.
Heatmiser were sonically interesting in the sense they really didn't have a set sound. They were more punky than the grunge bands when they started out but they slowly started to become many things: mostly what Elliott Smith's music would become as well as Neil Gust's. All in all they were at times kind of dull but for the most part when they wrote a good they really wrote a good song.
When the band was around they were kind of a bunch of misfits because they didn't fit in with the whole grunge trend too well and the media labeled them "Homocore" because Neil Gust was openly g
ay. They also weren't anywhere near as serious as the moody grunge bands around at the time, they often joked around on stage and then there was their name of course. All in all Heatmiser basically missed the success train and are more known for launching Elliott's career but they did have some influence on bands like Built to Spill and even Jimmy Eat World.
"The music was loud and kind of aggressive sounding compared to grunge. We were more into the DC bands that were going on then. Like the Discord bands. Basically we kind of wanted to be Fugazi, you know, but we didn’t sound anything like Fugazi." - Elliott Smith