I picked music I like now, as opposed to music I actually liked that year. I can't remember my favorite band at age 2, and I remember exactly what I was listening to in 1995 and it wasn't good.
1984 The Replacements- Let It Be
1985 Tom Waits- Rain Dogs
1986 They Might Be Giants- They Might Be Giants
1987 The Pastels- Up For A Bit With The Pastels
1988 The Go Betweens- 16 Lover's Lane
1989 Negativland- Helter Stupid
1990 Yo La Tengo- Fakebook
1991 The Magnetic Fields- Distant Plastic Trees
1992 Pavement- Slanted and Enchanted
1993 The Flaming Lips- Transmissions From The Satellite Heart
1994 Built To Spill- There's Nothing Wrong With Happiness
1995 The Apples in Stereo- Fun Trick Noisemaker
1996 Stereolab- Emperor Tomato Ketchup
1997 Ben Folds Five- Whatever and Ever Amen
1998 Cake- Prolonging The Magic
1999 Wilco- Summerteeth
2000 Elliott Smith- Figure 8
2001 Guided By Voices- Isolation Drills
2002 Spoon- Kill The Moonlight
2003 The Fiery Furnaces- Gallowsbird's Bark
2004 Joanna Newsom- The Milk-Eyed Mender
2005 Andrew Bird- The Mysterious Production Of Eggs
2006 Neko Case- Fox Confessor Brings The Flood
2007 Jens Lekman- Night Falls On Kortedala
2008 Destroyer- Trouble In Dreams