From the Choirgirl Hotel - Tori Amos
Savage Garden - Savage Garden
No Need to Argue - The Cranberries
Fallen - Evanescence
Three Cheers for Sweet Revenge - My Chemical Romance
Actor - St. Vincent
Alpinisms - School of Seven Bells
Funeral - Arcade Fire
Aeroplane Over the Sea - Neutral Milk Hotel
Born to Die - Lana del Rey

I didn't think I'd be able to come up with a full list (I tend to like a few songs rather than entire albums) but I did it! Listed in order of when they first made their appearance in my life in a meaningful way.