I didn't really get into music during my childhood but these are the albums that have shaped me in some way or at least resonated with me at the time.
Peter Gabriel - So - The first album that I owned. Initially got drawn in after seeing the Sledgehammer video but quickly fell in love with great songs like Red Rain and Mercy Street.
The Christians - The Christians - My brother bought this album but for a short time I played it to death, it just stood out from all the other music that was around at the time.
Nirvana - Nevermind - Like most teens at the time I was drawn to the sound of Nevermind. If I'm honest I never really like many of the songs but Smells Like Teen Spirit struck a chord.
Smashing Pumpkins - Mellon Collie And The Infinite Sadness - This was the album that just clicked with me and started my appreciation of music. Until I saw Zero being played live on MTV I had no idea of how good music could be. Seeing that was like a lightbulb going on in my head. I bought the album the day after and have played it to death ever since. Still my favourite album.
Smashing Pumpkins - Cherub Rock - MCIS might be my favourite but this is the album that started my lasting obsession with the band. I made a very good friend at university after a conversation about being die-hards fan of certain bands.
Catatonia - International Velvet - Both my friend and I fell in love with the voice of Cerys Matthews. They became the first band that I saw play live (at the Octagon) and that gig made me appreciate the experience of seeing a band live.
Fiona Apple - Tidal - I missed this album when it came out but saw Fiona Apple's Fast As You Can (from her second album) on TV and thought it was interesting enough to listen to other songs. Fortunately I bought the much superior first album. It didn't sound like I was expecting it to, it was so much better. From this point I started listening to a a wider variety of music.
Holst - The Planets - I picked up this compilation album which contained Holst's Planet Suite, some Beethoven and Barber's Adagio For Strings. I annoyed the hell out of my flatmates at the time but I loved playing this whenever I wanted to chill out or felt sad.
David Bowie - Best Of Bowie - Bought during a phase of listening to all the old greats I'd dismissed in my musical ignorance.
The Killers - Hot Fuss - Became closer to a female friend because of this. Not saying how though
-played this album sooo much then. Always a battle to get to the turntable/cassette player. I often made it. 
