Funny you should ask.  Aside from semi-random tracks on the iPod and on Facebook and PowerPop and other blogs, here's what I've been listening to:

The Kinks, "Autumn Almanac"
Fountains of Wayne, Sky Full of Holes
Steve Earle, I'll Never Get Out of This World Alive
Best Coast, Crazy for You
Adele, 21
My favorites of the 2000s, in no particular order:
drive-by truckers, a blessing and a curse
tegan and sarategan and sara, so jealous
the white stripes, white blood cells
bob dylan, modern times
fountains of wayne, welcome interstate managers
chris brokaw, incredible love
josh rouse, 1972
sufjan stevens, songs for christmas
shelby lynne, identity crisis
the avett brothers, mignonette

The twenty most-played songs/artists on my iPod (as of 2009 or so):
Chris Brokaw, "The Fields" and "Gauntlet"
Descendents, "I Like Food"
Josh Rouse, "It's the Nighttime" and "Winter in the Hamptons"
Shelby Lynne, "Your Lies"
Fountains of Wayne, "I Want an Alien for Christmas"
Dinosaur Jr., "Little Fury Things" and "Repulsion"
Drive-By Truckers, "Zoloft"
The Replacements, "Answering Machine" and "Favorite Thing"
The White Stripes, "Fell in Love with a Girl"
Bright Eyes, "First Day of My Life"
Prince, "Kiss" and "When Doves Cry"
Kelly Willis, "They're Blind"
Judas Priest, "You've Got Another Thing Comin' "
Dusty Springfield, "Just One Smile"
Bruce Springsteen, "Long Time Comin' "
Chris Brokaw, "I Remember"

I also recommend getting your own free personalized radio station on Pandora.com (this is such a great concept).

Patterson Hood of DBT covers most of The Boss's Darkness on the Edge of Town, live

Songs I wish were on my iPod (Listen up, Apple!):
Alex Chilton, "She Might Look My Way"
Amazing Rhythm Aces, "Third Rate Romance"
Mary Lou Lord, "Some Jingle Jangle Morning" (single version)

Some favorites of 2008 (more or less in order):
Flight of the Conchords
Drive-By Truckers, Brighter Than Creation's Dark
Good Old War
Lucinda Williams, Little Honey

Some favorites of 2007 (more or less in order):
Bruce Springsteen, Magic
 The Arcade Fire, Neon Bible
 Jason Isbell, Sirens of the Ditch
The White Stripes, Icky Thump
Wilco, Sky Blue Sky
Fountains of Wayne, Traffic and Weather
Lily Allen, Alright, Still
Bettye LaVette, The Scene of the Crime
My top albums of 2006:
1. Drive-By Truckers, A Blessing and a Curse
2. Bob Dylan, Modern Times
3. Sufjan Stevens, Songs for Christmas
4. Gnarls Barkley, St. Elsewhere
5. Lucero, Rebels, Rogues & Sworn Brothers

My top albums of 2005 (too hard to come up with five albums in this Age of iTunes):
1. Chris Brokaw, Incredible Love
2. Josh Rouse, Nashville
3. Bruce Springsteen, Devils and Dust 

My top five albums of 2004:
1. Tegan and Sara, So Jealous
2. Drive-By Truckers, The Dirty South
3. Patterson Hood, Killers and Stars
 4. Magnetic Fields, i
5. Elliott Smith, from a basement on a hill

My top five of 2003:
1. Josh Rouse, 1972
2. Drive-By Truckers, Decoration Day
3. Fountains of Wayne, Welcome Interstate Managers
4. Shelby Lynne, Identity Crisis
5. The White Stripes, Elephant

My top five of 2002:
1. Drive-by Truckers, Southern Rock Opera
2. Bruce Springsteen, The Rising
3. Neko Case, Blacklisted
4. Linda Thompson, Fashionably Late
5. Amy Rigby, World on a Broken String

My top five of 2001:
1. The White Stripes, White Blood Cells
2. Lucinda Williams, Essence
3. Chris Brokaw, red cities
4. Bruce Springsteen & the E Street Band, Live in New York
5. Ryan Adams, Gold

My top five of 2000:
1. Aimee Mann, Bachelor No. 2
2. Belle and Sebastian, Lazy Line Painter Jane
3. Marah, Kids in Philly
4. Shelby Lynne, I Am Shelby Lynne
5. Steve Earle, Transcendental Blues

My top five of 1999:
1. Fountains of Wayne, Utopia Parkway
2. Aimee Mann, Magnolia soundtrack
3. Magnetic Fields, 69 Love Songs
4. Beck, Midnite Vultures and Mutations
5. Kelly Willis, What I Deserve

My top five of 1998:
1. Lucinda Williams, Car Wheels on a Gravel Road
2. Sarge, The Glass Intact
3. Belle and Sebastian, The Boy with the Arab Strap
4. Cheri Knight, The Northeast Kingdom
5. Elliott Smith, XO

My top ten of the 1990s (in no particular order):
Lucinda Williams, Sweet Old World
Aimee Mann, I'm With Stupid
Fountains of Wayne, Utopia Parkway
Guided By Voices, Alien Lanes
Amy Rigby, Diary of a Mod Housewife
Freedy Johnston, Can You Fly
Nirvana, MTV Unplugged in New York
Blake Babies, Sunburn
Steve Earle, I Feel Alright
Iris DeMent, My Life

Desert Island Discs ... ours go up to Eleven

Last updated on 13 October 2011.  My thanks to Barefoot Jim Connelly for coming up with this idea so I could steal it.