I am a very big completist, so I like to have everything of my favourite artists:
Tori Amos: - Little Earthquakes; Under The Pink; Boys for Pele; From the Choirgirl Hotel; To Venus and Back.
Plus (gosh this is anal), 12" of Silent All These Years and some other singles.
Sophie B. Hawkins; Timbre (both versions); Whaler; and the other one (tongues and tails?)
Stereolab; Peng, The Groop Played...gosh, I must have about 11 or 12 0r even 13 Stereolab albums!
B-52's I have (counts in head) about 10 albums... plus I have 52 Girls about 4 times on different singles! Many other (vinyl) singles.
Sleater-Kinney: 5 albums,
Suede all their albums except Head Music which, after buying 'electricity' and knowing every inch of it after hearing it 3 times, decided not to purchase the album.
Lush; too many singles and albums! Really.
Aimee Mann; Whatever; I'm With Stupid; Bachelor; Magnolia
Somehow I have ALL THREE Dubstar albums! All three Sundays albums....
Throwing Muses: 4
The Smiths: 5
Luscious Jackson: 4
I too have 3 Enya albums!
I could go on, but I won't. Cause it's boring, and I can't remember anything anymore.