Can someone compile a list of the longest running #1s from this decade?
Really depends on what you want to call a decade. For most people, the decade ends on December 31, 2009. (Which, according to the calendar is false, but it is accepted as the end of the pop culture decade.) According to the calendar, the decade ends on December 31, 2010, since there was no year 0. But, since this is a music forum, I'm going to assume you mean a pop culture decade.
11 weeksMariah Carey "We Belong Together" (2005)
10 weeks*Nsync "Bye, Bye, Bye" (2000)
Leona Lewis "Bleeding Love" (2008)
9 weeksChristina Aguilera "Lady Marmalade (feat. Lil' Kim, Mýa, and P!nk)" (2001)
8 weeksNickelback "How You Remind Me" (2001/2002)
Avril Lavigne "Complicated" (2002)
Hoobastank "The Reason" (2004)
Nelly "Over and Over (feat. Tim McGraw)" (2004/2005)
Nelly Furtado "Promiscuous (feat. Timbaland)" (2006)
Fergie "Big Girls Don't Cry" (2007)
7 weeksDestiny's Child "Independent Woman (Part 1)" (2000/2001)
Shaggy "Angel (feat. Rayvon)" (2001)
OutKast "Hey Ya!" (2003/2004)
Kelly Clarkson "Since U Been Gone" (2005)
Shakira "Hips Don't Lie (feat. Wyclef Jean)" (2006)
Timbaland "Apologize (feat. OneRepublic)"/OneRepublic "Apologize" (2007)
6 weeks*Nsync "It's Gonna Be Me" (2000)
Linkin Park "In the End" (2002)
Eminem "Lose Yourself" (2002)
Kelly Clarkson "Miss Independent" (2003)
The Black Eyed Peas "Where Is the Love? (feat. Justin Timberlake)" (2003)
JoJo "Leave (Get Out)" (2004)
Gwen Stefani "Hollaback Girl" (2005)
Beyoncé "Check on It (feat. Slim Thug and Bun B)" (2006)
Beyoncé "Irreplaceable" (2006/2007)
Timbaland "The Way I Are (feat. Keri Hilson and The D.O.E.)" (2007 - non-consecutive)
Flo Rida "Low (feat. T-Pain)" (2008)
The Black Eyed Peas "Boom Boom Pow" (2009)
The Black Eyed Peas "I Gotta Feeling" (2009)
5 weeksSavage Garden "I Knew I Loved You" (2000)
3 Doors Down "Kryptonite" (2000)
Creed "With Arms Wide Open" (2000)
Blu Cantrell "Hit 'Em Up Style (Oops)" (2001)
Alicia Keys "Fallin'" (2001)
Vanessa Carlton "A Thousand Miles" (2002)
Nelly "Dilemma (feat. Kelly Rowland)" (2002)
Justin Timberlake "Rock Your Body" (2003)
Maroon 5 "She Will Be Loved" (2004)
Mariah Carey "Shake It Off" (2005)
Chris Brown "Run It!" (2005/2006)
Justin Timberlake "SexyBack (feat. Timbaland)" (2006)
Gym Class Heroes "Cupid's Chokehold (feat. Patrick Stump)" (2007)
Jesse McCartney "Leavin'" (2008)
Chris Brown "Forever" (2008)
Lady GaGa "Poker Face" (2009)
4 weeksMacy Gray "I Try" (2000)
O-Town "All or Nothing" (2001)
P!nk "Don't Let Me Get Me" (2002)
Christina Aguilera "Beautiful" (2003)
Jennifer Lopez "All I Have (feat. L.L. Cool J)" (2003)
50 Cent "In Da Club" (2003)
Beyoncé "Baby Boy (feat. Sean Paul)" (2003)
Britney Spears "Toxic" (2004)
Usher "Yeah! (feat. Lil' Jon and Ludacris)" (2004)
Ashlee Simpson "Pieces of Me" (2004)
Green Day "Boulevard of Broken Dreams" (2005)
Kelly Clarkson "Because of You" (2005 - non-consecutive)
Mary J. Blige "Be Without You" (2006)
Justin Timberlake "My Love (feat. T.I.)" (2006)
Nelly Furtado "Say It Right" (2007)
P!nk "U + Ur Hand" (2007)
Justin Timberlake "Summer Love" (2007)
Alicia Keys "No One" (2008)
Rihanna "Disturbia" (2008)
P!nk "So What" (2008)
The All-American Rejects "Gives You Hell" (2009)
3 weeksBritney Spears "Oops!...I Did It Again" (2000)
Destiny's Child "Jumpin', Jumpin'" (2000)
Lenny Kravitz "Again" (2001 - non-consecutive)
Janet Jackson "All for You" (2001)
Jennifer Lopez "I'm Real (feat. Ja Rule)" (2001)
Mary J. Blige "Family Affair" (2001)
Avril Lavigne "I'm With You" (2003)
Nelly "Shake Ya Tailfeather (feat. P. Diddy and Murphy Lee)" (2003)
3 Doors Down "Here Without You" (2003 - non-consecutive)
OutKast "The Way You Move (feat. Sleepy Brown)" (2004)
Mario "Let Me Love You" (2005)
Sean Paul "Temperature" (2006 - non-consecutive)
Hinder "Lips of an Angel" (2006)
Chris Brown "With You" (2008)
Katy Perry "Hot N Cold" (2008)
Beyoncé "Single Ladies (Put a Ring on It)" (2009)
Lady GaGa "LoveGame" (2009)
2 weeksNine Days "Absolutely (Story of a Girl)" (2000)
Jennifer Lopez "Love Don't Cost a Thing" (2001 - non-consecutive)
Jennifer Lopez "Ain't It Funny (feat. Ja Rule)" (2002)
Nelly "Hot In Herre" (2002)
Avril Lavigne "Sk8er Boi" (2002)
No Doubt "Underneath It All (feat. Lady Saw)" (2002)
Beyoncé "Crazy In Love (feat. Jay-Z)" (2003)
Jessica Simpson "With You" (2004)
Maroon 5 "This Love" (2004)
Kanye West "Gold Digger (feat. Jamie Foxx)" (2005)
The Pussycat Dolls "Stickwitu" (2006)
The Pussycat Dolls "Buttons (Remix) (feat. Snoop Dogg)" (2006)
Nickelback "Far Away" (2006)
Daughtry "It's Not Over" (2007)
Kanye West "Stronger" (2007)
Sara Bareilles "Love Song" (2008)
Rihanna "Take a Bow" (2008)
T.I. "Live Your Life (feat. Rihanna)" (2008/2009 - non-consecutive)
Flo Rida "Right Round (feat. Ke$ha)" (2009)
3OH!3 "Don't Trust Me" (2009)
1 weekChristina Aguilera "What a Girl Wants" (2000)
Backstreet Boys "She Me the Meaning of Being Lonely" (2000)
Eve "Let Me Blow Ya Mind (feat. Gwen Stefani)" (2001)
No Doubt "Hey Baby (feat. Bounty Killer)" (2002)
Eminem "Without Me" (2002)
3 Doors Down "When I'm Gone" (2003)
R. Kelly "Ignition" (2003)
Evanescence "Bring Me to Life (feat. Paul McCoy)" (2003)
Kelly Clarkson "Breakaway" (2004)
Gavin DeGraw "I Don't Wanna Be" (2005)
Ciara "1, 2 Step (feat. Missy Elliott)" (2005)
D.H.T. "Listen to Your Heart" (2005)
Ne-Yo "So Sick" (2006)
Rihanna "SOS" (2006)
Justin Timberlake "What Goes Around... Comes Around" (2007)
Avril Lavigne "Girlfriend" (2007)
P!nk "Who Knew" (2007)
Jason Mraz "I'm Yours" (2008)
Britney Spears "Womanizer" (2009)
Lady GaGa "Just Dance (feat. Colby O'Donis)" (2009)
Taylor Swift "Love Story" (2009)
Britney Spears "Circus" (2009)
Katy Perry "Waking Up In Vegas" (2009)
Taylor Swift "You Belong with Me" (2009)
Kings of Leon "Use Somebody" (2009)