I'll give this a go.
2009: The Antlers- Hospice
2008: Why?- Alopecia
2007: Nujabes- Hydeout Collections Vol. 2
2006: The Sound of Animals Fighting- Lover, the Lord has Left Us
2005: The Mars Volta- Frenches le Mute
2004: MF DOOM- Mm...Food?
2003: The Mars Volta- De-loused in the Comatorium
2002: The Flaming Lips- Yoshimi Battles the Pink Robots
2001: System of a Downs- Toxicity
2000: At the Drive-In- Relationship of Command
1999: Sigur Ros- Agaetis Byrjun
1998: System of a Down- System of a Down
1997: Cornelius- Fantasma
1996: Beck- Odelay
1995: The Flaming Lips- Clouds Taste Metallic
1994: Green Day- Dookie (honestly though my birthyear was pretty weak musically)
1993: Bjork- Debut
1992: Death In June- But, What Ends When the Symbols Shatter?
1991: My Bloody Valentine- Loveless
1990: Mike Oldfield- Amarok
1989: Red Hot Chili Peppers- Mother's Milk
1988: Public Enemy: It Takes a Nation etc
1987: The Flaming Lips- omgawd
1986: The Smiths- Queen is Dead (by far the hardest one of the decade)
1985: The Smiths- Meat is Murder
1984: The Smiths- Hatful of Hollow (I'm not even a huge Smiths fan, the 80s are just a really rough time for my music collection.
)
1983: Toy Dolls- Dig that Groove, Baby
1982: Violent Femmes- S/T
1981: Rush- Moving Pictures
1980: Rush- Perm Waves
1979: Frank Zappa- Sheik Yerbouti
1978: Sun Ra- Lanquidity
1977: David Bowie- Low
1976: Rush- 2112
1975: Queen- A Night at the Opera
1974: Frank Zappa- Apostrophe'
1973: Stevie Wonder- Innvervisions
1972: Yes!- Close to the Hedge
1971: Comus- First Utterance
1970: Nick Drake- Bryter Layter
1969: Frank Zappa- Hot Rats
1968: Aretha Franklin- Aretha Now
1967: The Velvet Underground- The Velvet Underground + The main attraction
1966: Frank Zappa/Mothers- Freak Out!
1965: Bob Dylan- Highway 61 Revisited
1964: Andrew Hill- Black Fire
1963: Charles Mingus- The Black Saint and the Sinner Lady
1962: Nothing!