Here are various Thundercats and characters and the song that best represents them (in my not so humble opinion).

Tygra - "Marijuana in your Brain" - Lords of Acid
Lion-O - "Pretty Fly (for a white guy)" - Offspring
Panthro - "Pimpin' Ain't Easy" - Ice-T
Cheetara - "I Can't Drive 55" - Sammy Hagar
Kat - "Smoking in the Boys Room" - Motley Crew
Kit - "A Little Bit Dangerous" - Roxsette
BenGali - "The Warrior" - Patty Smith
Pumyra - "Don't you (forget about me)" - Simple Minds
Lynxo - "Blind" - Korn
Snarf - "Don't Worry be Happy" - Bobby McFerrin
Snarfer - "Hot Rocket Baby"

Mumm-Ra - "Walk like an Egyptian" - The Bangles

Mandora - "Through the Eyes of a Pig" - Cypress Hill

Grune - "Natural Born Killaz" - Ice Cube and Dr. Dre

Jagga - "The Asshole Song" - Jimmy Buffet

Slythe - "Whip it" - Devo
Monkian - "Day-O (Banana Boat Song)" - Harry BelaFonte
Jacalman - "coward" - Holly Mcnarland
Vultureman - "Weird Science" - Oingo Boingo

Luna - "The Bitch is Back" - Elton John
Amuk - "Candyman" - Aqua
Chilla - "Cold as Ice" Foreigner
Tugmug - "Jump" - Van Halen
Alluro - "I Put a Spell on You" - CCR
Redeye - "Private Eyes" - Hall 'n Oats

Axell - "Deadly Assassins" - Everlast
Chanur - "Outcast" - LK2 Soundtrack
Fianna - "Dogs" - Pink Floyd
Fuzzy - "my mind is playing tricks on me" - Ghetto Boys
Kamanchee - "Friend or Foe" - Adam ant
Mad Bassist - "2am" - Iron Maiden
Mittens - "All I really Want" - Alanis Morriset
PeachyRa - "The Look" - Roxsette
Purrsia - "Mickey" - Toni Basil
Queen - "Bitch" - Meredith Brooks
RD - "No Respect" Kool Moe Dee
Ruka - "When the Tigers Broke Free" - Pink Floyd
Shark - "Pool Shark" - Sublime
Spark - "I've Got the Power" - Snap
Tara - "#1 Crush" - Garbage
Tayindin - "The Child Inside" - Qkumba Zoo
ThunderWolf - "Insane in the Brain" - Cypress Hill --- "I'm an Asshole" - Denis Leary
Zhie - "911 is a joke" - Public Enemy
Zhyan - "Avenging Angels" - Space

Whiddaw - "Looser" - Beck
John Doe - "Why's Everybody Always Pickin' on Me" - Blood Hound Gang