[CaptHayfever]

^^See, Al neither made nor authorized that "Ebay" video.

from "Weird Al" Yankovic:
Ricky
I Love Rocky Road

from Eat It:
Eat It
I Lost on Jeopardy

from Dare to Be Stupid:
Like a Surgeon
Dare to Be Stupid
One More Minute
This is the Life

from Polka Party!:
Living with a Hernia
Christmas at Ground Zero

from Even Worse:
Fat

from UHF:
Money For Nothing/Beverly Hillbillies*
UHF

from Off the Deep End:
Smells Like Nirvana
You Don't Love Me Anymore

from Alapalooza:
Jurassic Park
Bedrock Anthem

A single not from any album at all:
Spy Hard
Headline News

from Bad Hair Day:
Amish Paradise
Gump

from Running with Scissors:
The Saga Begins
The Weird Al Show Theme
It's All About the Pentiums

from Poodle Hat:
Bob

from Straight Outta Lynwood:
White & Nerdy
Pancreas
I'll Sue Ya
Virus Alert
Weasel Stomping Day
Close But No Cigar
Do I Creep You Out
Trapped in the Drive-Thru
Don't Download this Song

Other non-canon authorized videos:
Another One Rides the Bus (live)
Livin' in the Fridge (partial)
Lasagna (partial)
Polka Power
Homer & Marge
Hardware Store
Angry White Boy Polka

*The asterisk doesn't actually mean anything; it's in the song title for legal reasons.

And remember, "I'm-a Luigi, number one!"