I listened to his show from December 1988 until the big thinkers at KLSX removed him from the airwaves. (Now I don’t know what L. A. station carries his show. :()
But there are some titles he played, whose artists I never identified:
“The Schnauzer”–modeled on Simon & Garfunkel’s “The Boxer,” a bittersweet dog ballad.
“Borderline”–country western style with rather aimless lyrics; singer was a young woman.
“O-Vlade-O-Divac,” after the Beatles’ hit “Obla-D-Obla-Da,” celebrating the Lakers’ former Yugoslav center.
“Silver Bells”–a version alluding to the madness of the Christmas shopping season.
“[Elvis Sightings]”–title also unknown; sung in 3/4 time before a live (and appreciative) audience; the lyrics are hypothetical tabloid headlines about The King, including “Elvis gave AIDS to my dog.”
“Running Wild”–Dr. D said that Spike Jones recorded this on an obsolete medium and that he could only play part of the recording–featuring an ocarina, a clarinet and a banjo–on a standard phonograph. What kind of machine was it?
“Chinese Waiter,” by Buddy Hackett. I never did know the actual title.
“I Think I’m a Clone Now”–by Weird Al Yankovic. I at first thought the original, “I Think We’re Alone Now,” was by the Rolling Stones…
Can any Dopers answer these questions for me please? 
Actually, ‘I Think I’m A Clone Now’ is a parody of Tiffany’s version of the Bobby Shondell classic “I Think We’re Alone Now”
Thanx
You can search playlists back to 1980 (and some 70’s) at http://php.indiana.edu/~jbmorris/playlists.html . And when Zack’s Stacks comes back up (check the newsgroup below), you might be able to get MP3s of the things you want.
I tried a search on “schnauzer”, but got no hits.
A search for “hackett” produced a few hits, among which was this most recent airing: “drd94.0515.html:The Chinese Waiter - Buddy Hackett”
Subscribe to the USENET newsgroup rec.music.dementia! You can check there for places to listen to it on the Internet.
Actually, that’s Tommy James and the Shondells.
Is Dr. Demento’s show still alive and kicking? It’s been a long time since I heard “Dead Puppies.”
I am still looking to find you have 254 messages. I heard it a few weeks ago and laughed my ass off.
I can still hear Dr. Demento on Sundays, but it goes in and out from crappy reception since I live by a few different radio stations and television stations. 
I logged onto that website and I am immensely impressed. However, since I listened to Dr. D in the Los Angeles area, I heard a version of his show different from the syndicated version heard everywhere else, and some of the titles I sought weren’t on those playlists.
So I sent them an e-mail to ask for the titles apparently Angelenos only heard.