I'll make a VERY short list.
"Beggar's Banquet" - the Rolling Stones
"Muddy and the Wolf" Chess Records compilation
"Unplugged in New York" - Nirvana
"Crystal Planet" - Joe Satriani
"Mule Variations" - Tom Waits
"Boys and Girls in America" - The Hold Steady.
Beggar's Banquet was the Stones album my dad played around the house the most when I was a kid, and more than any other album I could think of was the album that made me realize that whatever this "music" thing was was something I wanted to be a part of.
That Chess records compilation was the first blues album I ever heard - it was a compilation of a few tracks from the Wolf London Sessions with the Stones rhythm section and Eric Clapton on lead guitar, and a similar recording with Waters and the Butterfield Blues Band. The Waters section actually kind of sucked, aside from a killer live recording of "Long Distance Call," but that album was what really made me start to get into the sound of the guitar.
Then there's "Unplugged in New York" - I'd already been a little infatuated, from afar, by the guitar by the time I heard that album, but Kurt Cobain was the guy who made it seem like something attainable, that I could actually do
. I was listening to guys like Hendrix by then and was totally drawn into the sound of the guitar, but Hendrix seemed light years removed from what mere mortals like me could do. Cobain however was more of an anti-guitar-hero, and that album was what got me to actually pick up the guitar and give it a go.
Crystal Planet was my first Satriani album, which I bought after hearing a live recording of "Always with Me, Always with You" on a radio station and being blown away by what I was hearing. Needless to say, it had a sliiiiiight impact on my approach.
"Mule Variations" was definitely an acquired taste... And that's another really long story in its own right. However, I consider Waits both one of my favorite songwriters and one of my favorite vocalists. If I could sing, that album is what I'd want to sound like.
And "Boys and Girls..." was just one of those albums that kind of becomes a soundtrack for a period of your life. Call it from 2005-2010 or so... Craig Finn is also an incredible lyricist - the opening two lines of the chorus - "She was a really cool kisser, and she wasn't very strict of a Christian./She was a damned good dancer, but she wasn't all that great of a girlfriend," are just perfect - I don't know anyone who hasn't wanted a woman like that in their lives, if even for only a night.