I finally got a top ten:

(Note: 4-7 are tied)

1. Red Hot Chili Peppers

Genre: Funk Rock 

1983-Present

Top Ten Songs: "I Could Have Lied", "Blood Sugar Sex Magik", "Can't Stop", "Wet Sand", "Readymade", "Under the Bridge", "21st Century", "Californication", "Give it Away", "Fight Like a Brave"

2. Bad Religion

Genre: Punk Rock

1980-1984, 1986-Present

Top Ten Songs: "Generator", "Come Join Us",  "Sinister Rouge", "Along the Way", "Sorrow", "American Jesus", "Infected", "Atomic Garden", "We're Only Gonna Die", "F**k Armageddon...This is Hell" 

3. Social Distortion

Genre: (Early) Punk Rock

1979-1985, 1986-Present

Top Ten Songs: "Story of My Life", "Reach for the Sky", "Don't Take Me For Granted", "Ring of Fire", "Ball and Chain", "Angel's Wings", "Winners and Losers", "Footprints on My Ceiling", "Mommy's Little Monster", "Live Before You Die"

4. Jack Johnson

Genre: Soft Rock

1999-Present

Top Ten Songs: "Bubble Toes", "Flake", "Banana Pancakes", "No Other Way", "Better Together", "Posters", "Upside Down", "Gone", "Rodeo Clowns", "Good People"

5. Bob Marley and the Wailers

Genre: Reggae

1962-1981

Top Ten Songs: "Stir it Up", "Kaya", "One Love", "Jamming", "Crisis", "No Woman No Cry", "Easy Skanking", "Redemption Song", "Time Will Tell", "Is This Love"

6. Jimi Hendrix (The Jimi Hendrix Experience)

Genre: Rock

1966-1970

Top Ten Songs: "Fire", "Purple Haze", "The Wind Cries Mary", "The Star Spangled Banner", "Foxey Lady", "Are You Experienced?", "I Don't Live Today", "Castles Made of Sand", "Hey Joe", "Can You See Me"

7. Nirvana

Genre: Grunge

1987-1994

Top Ten Songs: "Lake of Fire", "Come As You Are", "All Apologies", "Smells Like Teen Spirit", "In Bloom", "Lithium", "Something in the Way", "Rape Me", "Drain You", "Polly"

8. Smashing Pumpkins

Genre: Hard Rock

1988-2000, 2006-Present

Top Ten Songs: "Bullet With Butterfly Wings", "Today", "1979", "Zero", "Muzzle", "Mayonaise", "Disarm", "Geek USA", "Silverf*ck", "Tonight, Tonight"

9. Sublime

Genre: Skunk (Ska/Punk)

1988-1996

Top Ten Songs: "Santeria", "Badfish", "What I Got", "Boss D.J.", "Rivers of Babylon", "We're Only Gonna Die From Our Own Arrogance", "Same in the End", "Smoke Two Joints", "Date Rape", "40 oz. to Freedom"

10. Pennywise

Genre: Punk Rock

1988-Present

Top Ten Songs: "F**k Authority", "Bro Hymn", "Yell Out", "Knocked Down", "Closer", "Unknown Road", "Slow Down", "Yesterdays", "God Save the USA", "The Kids"