There's probably too many for me to list, but I'll give it a shot. In order of appearance...
"Please Don't Touch" -
Brian Setzer Orchestra version
"Mack The Knife" "Beyond The Sea"-
Bobby Darin"In Shreds" "Mad Jack" "Soul In Isolation" and "Swamp Thing" -
The Chameleons"Brown Derby Jump" "Come Back To Me" "Don Quixote" "Here Comes The Snake" and "So Long Toots" -
Cherry Poppin Daddies"The Long Black Veil" -
The Chieftians with the Rolling Stones"Afternoons and Coffeespoons" -
Crash Test Dummies"O Fortuna(Carmina Burana) -
Carl Orf"Millionaire's Holiday" -
Combustible Edison"Kyoto Song" "Like Cockatoos" "The Blood" "The Hanging Garden" -
The Cure"Saltarello" -
Dead Can Dance"Sick and Tired" "Deny" -
Default"The Fishing Song" -
Ditch Bank Okies"Nocturnal Me" -
Echo & The Bunnymen"Acrobat" "Clown Show" "Without Within" -
Ednaswap"My Dark Life" -
Elvis Costello & Brian Eno"At Last" "These Foolish Things" -
Etta James"Easy As Sin" "Native Land" -
Everything But The Girl"Everyday Sunshine" "Party At Ground Zero" -
Fishbone"100 Years" -
Five For Fighting"Atom Bomb" -
Fluke"The World Is Not Enough" -
Garbage"Airport Song" -
Guster"White Trash" -
Hillbilly Hellcats"Down In the Tube Station at Midnight" "Strange Town" "Town Called Malice" -
The Jam"The Eternal" "Day Of The Lords" -
Joy Division"You Belong To Me" -
Jason Wade version
"Juke Joint Jezebel" "UNFIT" -
KMFDM"Light as the Breeze" "Democracy" "The Future" -
Leonard Cohen"Romeo Had Juliette" -
Lou Reed"Black Betty" -
Ram Jam, Lynyrd Skynyrd or Tom Jones"I Try" -
Macy Gray"Papa Won't Leave You Henry" "Straight to You" "The Curse of Millhaven" "Lament" -
Nick Cave"Feelin Good" "Here Comes The Sun" "I Want a Little Sugar In My Bowl" -
Nina Simone"Turn Me On" "The Long Day Is Over" "Don't Know Why" -
Norah Jones"All I Need Is Everything" "Conjectures of a Guilty Bystander" -
Over The Rhine"The Sickbed of Cuchulainn" "Wildcats of Kilkenny" -
The Pogues"Marie Celeste" "Make a Circuit with Me" "I'm Ready" "Rockabilly Guy" -
The Polecats"Glory Box" -
Portishead"Cruel" "Appetite" "Desire As" "Goodbye Lucile (Johnny Johnny)" "When The Angels" -
Prefab Sprout"Twilight Time" -
The Platters"When Worlds Collide" -
Powerman 5000"Creep" "Fake Plastic Trees" -
Radiohead"Dig Ophelia" "Transylvanian Concubine" "Why Don't You Do Right" -
Rasputina"Crawling Mantra" "Hand on Heart" "Talk About The Weather" "Walking On Your Hands" -
Red Lorry Yellow Lorry"Down With The Sickness" -
Richard Cheese version, and Disturbed
"Dragula" "House of 1000 Corpses" "Living Dead Girl" "Devil Man" -
Rob Zombie"Zip Gun Bop" -
Royal Crown Revue"Attack Ships on Fire" "Beers Steers & Queers" "Do Ya Think I'm Sexy" -
Revolting Cocks"Always" -
Saliva"Danny Boy" "Roddy McCorley" "Donegal Express" "My Way" -
Shane MacGowan"Alice" "First and Last and Always" "Marian" "Nine While Nine" "Temple of Love" "Valentine" -
Sisters of Mercy"Selling Jesus" -
Skunk Anansie"Circles" "Screen Writers Blues" "Sugar Free Jazz" "Super Bon Bon" -
Soul Coughing"St. James" -
Snakefarm"Man of Constant Sorrow" -
Soggy Bottom Boys 
"Here Without You" "When I'm Gone" -
Three Doors Down"9th & Hennepin" "Cemetery Polka" "Flowers Grave" Jockey Full of Bourbon" "Rain Dogs" "Singapore" "Walking Spanish" -
Tom Waits"Into the Mystic" -
Van Morrison"Low Rider" -
War"Happy Jack" -
The Who"Common People" -
William Shatner 
"Poor Little Girl" -
X"Dear God" -
XTC