For some reason I find it fascinating to know which album of particular bands/artists that people first bought. For one thing that first album that you buy determines how much you like (or don't like) the band, but it can also completely colour your view of a band.
With some bands like the Clash I bought a lot of singles before I ever owned one of their albums. The first LP I bought of theirs was London Calling, but I bought and still own most of their early singles.
other albums that I got as a teenager were happy accidents, records or tapes bought second hand that awakened my interest in a band. The first of these was Houses of the Holy by Led Zeppelin, an LP that I bought off of my parents friend George. It was interesting to have this as my first Zep as it is a lot more mellow than most of their stuff. From the same friend I also bought a pre-recorded tape of Aladin Sane by David Bowie and so my life long love affair with David Bowie began and I quickly followed this purchase with Ziggy Stardust and Space Oddity. I bought the aforementioned bowie LPs with my birthday money from a mail order record company (I must have been 13 or 14) and at the same time I got A farewell to Kings by Rush. An album that would hardly be off of my turntable for the next couple of years.
I think often (well for me anyway) the first album you buy by a band will remain your favourite - like Abbas Arrival, which I owned when I was 12 and repurchased on cd recently. There are exceptions to this though, my first Yes LP was Close to the Edge but if I play Yes now it is more likely to be the album 2112.
The Smiths - The Smiths
Captain Beefheart - Blue Jeans and Moonbeams
Crosby Stills Nash & Young - So Far
Genesis - And then There Were Three (my favourite now though is probably Abacab)
Hawkwind - Live 79
Deep Purple - 24 Carat Purple
Pink Floyd - Relics
Fleetwood Mac - Rumours
Of course sometimes the first album that you buy by an artist is the only album of theirs that you purchase, either because you are not so keen on their other stuff (for example I love Wave by Patti Smith but am not keen on her other albums) or you just grow up and move on...examples of this are Yazoo and the Thompson Twins (yes I really did!)