Stole this idea from Jelone. He had an idea to list his favorite album from each year of his life, and being low on creative energy I have no choice but to plagiarize.First, here's his.

Now, here's mine.

1986- Talking Heads - True Stories
1987- R.E.M. - Document
1988- The Dead Milkmen - Beelzebubba
1989- Bad Religion - No Control
1990- Primus - Frizzle Fry
1991- Mr. Bungle - self-titled
1992- Faith No More - Angel Dust
1993- Beck - Golden Feelings
1994- Pizzicato Five - Made in USA
1995- Rancid - ...And Out Come the Wolves
1996- Weezer - Pinkerton
1997- Primus - Brown Album
1998- the pillows - Little Busters
1999- Cibo Matto - Stereo Type A
2000- Barenaked Ladies - Maroon
2001- John Zorn - The Gift
2002- Boris - Heavy Rocks
2003- Polysics - National P
2004- Flogging Molly - Within a Mile of Home
2005- Deerhoof - Runners Four
2006- Cheer-Accident - What Sequel?
2007- Melt-Banana - Bambi's Dilemma
2008- Cyro Baptista - Banquet of the Spirits

Tough decisions for a lot of these years. Here are a whole bunch of runners-up, very noteworthy albums that deserve honorable mention:
1988- Sonic Youth - Daydream Nation
1991- Dire Straits - On Every Street
1997- Faith No More - Album of the Year
David Byrne - Feelings
2003- Melt-Banana- Cell-Scape
2004- David Byrne - Grown Backwards
2005- Fantômas - Suspended Animation
2006- Peeping Tom - self-titled
2007- Deerhoof- Friend Opportunity
Mark Knopfler - Kill to Get Crimson
2008- Flogging Molly - Float

Keep in mind these are my favorite albums from each year. Totally independent of how influential they were. Each album holds a fond place in my heart, mostly prompting me to go back to my earlier tastes.

Edit: On second thought, I can't believe I forgot Vision Creation Newsun by Boredoms (released 1999). Seriously, it almost beas out Stereo Type A for me. But I can't decide which is better.