My ten, in no order...
Pink Floyd - Wish You Were Here - It was the first Floyd that I listened to that wasn't Dark Side or the Wall and boy did open doors for me.
Led Zeppelin - IV - Speaking of opening doors... This album was the first classic rock album I ever really listened to. While I criticize Zeppelin to no end these days, I owe them quite a bit.
Radiohead - Kid A -
Neutral Milk Hotel - Aeroplane - It's hipster trash and it's STILL better than your favorite album.
The Strokes - Is This It? - Similar to Zeppelin IV in that it had a HUGE influence on what I listen to, but I still give this album regular spins.
Sigur Ros - () - The first post rock band I got into, and the album that can only be described as beautiful.
Mogwai - Happy Songs for Happy People - Let it be known if I could have one song to listen to for the rest of time that song would be "Hunted by a Freak."
The Smiths - The Queen is Dead - There was a point when I tried listening to this like 2 years ago and just found it unbearable. I revisited The Smiths 6 months or so ago and discovered that they are gods. After listening to this and enjoying it, I found myself able to listen to a lot of things I otherwise wouldn't have gotten around to.
The Mars Volta - De-loused in the Comatorium - I SHOULD NOT like this band. They are far different than anything that I listen to, yet they are among my favorites. This is their best work, though not by far.
Jeff Buckley - Grace - Perfection.
A very safe list, but I think these 10 albums have had a bigger impact on who I am today musically. All led me down roads that I would have otherwise never gone down. Loveless, The Velvet Underground & Nico, and Piper at the Gates could all very well have been on this list too.