I like the Frank Zappa pastiche, “Genius in France” from Poodle Hat.
My favoite Al song of all is “Frank’s 2000" TV” off Alapalooza.
“Albuquerque” is probably the funniest thing I’ve ever heard, but I hesitate to call it a “song,” really. (Ahhh, close enough, add my vote.)
“Melanie” from Even Worse got me started on his non-parodies.
I think his original stuff tends to be far funnier than his parodies. “One More Minute With You” is original, isn’t it? That one gets me every time.
I think his originals tend to be better than the parodies. Amongst my favorites:
- Buckingham Blues
- Happy Birthday
- The Check’s in the Mail
- Mr. Frump in the Iron Lung
- Buy Me a Condo
- One More Minute
- This Is the Life
- Dog Eat Dog
- Christmas at Ground Zero
- You Don’t Love Me Anymore
- Talk Soup
- My Baby’s in Love with Eddie Vedder
- Bob
My geek flag has never flown so high.
There’s also Trigger Happy, a style parody of the Beach Boys, but an original song. I like to sing it while playing shooting games, which I’m sure is giving an anti-video game violence campaigner a heart attack somewhere.
Fair enough. I have to admit I’m biased against that song because it is such a blatant rip off of “Skeet Surfin’” from the movie “Top Secret!” sung by none other than Val Kilmer(!)
Harvey the Wonder Hamster?
That’s OK, I went rabbit hunting with “The Ride Of The Valkyries” blaring at full volume on the 4WD’s stereo once. 
I love the smell of smokeless powder in the evening. 
Shooting at rabbits in time with the 1812 Overture is also considerably more fun than it should be, too…
As for Weird Al… “Alberquerque” is one of my favourite songs, and Running With Scissors is one of the very rare albums- by any artist- on which I like almost every song.
My two favorite Weird Al originals are “When I Was Your Age” and “Nature Trail to Hell.” IMO, the former can stand on its own as a real (non-comedy-type) song, if you don’t listen too closely to the lyrics.
Other favorites include “Hardware Store,” “Christmas at Ground Zero,” “Frank’s 2000-Inch TV,” “I’ll Be Mellow When I’m Dead,” “The Night Santa Went Crazy,” and “Truck-Drivin’ Man.”
Took me a long time to realize that “The Biggest Ball of Twine in Minnesota” was a style parody (and a very good one!) of Harry Chapin’s “30,000 Pounds of Bananas.”
If you like Weird Al, and you like World of Warcraft, these will make you smile a lot:
“You Make Me” is a great song. (“You make me want to staple bagels to my face…”)
“Melanie” is original, isn’t it?
Just chiming in with another thumb up for The Biggest Ball of Twine in Minnesota. I’ve now been to Minnesota TWICE without visiting the twineball. I’m ashamed of myself 
Dopers posting to this Thread might be interested in Make the Rock Hall Weird a fan-driven campaign to get him into the Rock n’ Roll Hall of Fame.
And the petition site informs me that the new Album is due in late September, and available for pre-order from Amazon!
Picking my favorite non-parody “Weird Al” song is too tough, so I’ll deviate from other folks’ picks and toss a ballot to Polkamon. Pokemon + polka + Al = TEH FUNNY!