I remember one during the Iran hostage crisis where he interviewed the Ayatollah.
I don’t know if it’s available on iTunes, but eMusic has his “Greatest Hits” record available for download. It’s got most/all of the ones mentioned here so far.
It was pretty funny when Chris Rock did it.
Reporter: OJ, where are you from?
OJ: Straight Outta Compton!
Reporter: And when you got rich, where did you move?
OJ: Straight Outta Compton!
Of course I was maybe 16 at the time. Anything that came out of Chris Rock’s mouth was funny.
I remember one that featured an interview with King Kong.
Now I was a lad of tender years during the mid 70’s when these songs were regularly featured on the radio. I remember that I knew these were meant to be funny but the humor was a touch ahead of my grasp and I often felt the contrast of the straight-man interviewer’s questions and then the off-beat musical answers to be somewhat jarring and maybe just a tad creepy.
Hey, I was a kid.
I remember when British Comedian, the late great Kenny Everett “interviewed” the Bee Gees.
(Note: he impersonated them)
Interviwer: How would you describe your teeth?
The Bee Gees : Maaaaaas - a chew sets
Interviwer : Oh, I see, its a joke.
The Bees Gees : It’s a tragedey,
etc.
Watergrate, the best one, IMO. It actually came out while Nixon was still in office, in 1973.
Mr. President, what were you doing at the time that the incident took place?
(Drinkin’ Wine Spo-De-O-Dee, Drinkin’ Wine)
And how do you feel about it now?
(Here I am, stuck in the middle)
Mr. President, what will your position be from now on?
(No more Mr. Nice Guy, no more Mr. Clean)
As a relatively unrelated aside, Drag City Records recently released this sort of thing as a promotional tool for Will Oldham and The Silver Jews.
Somebody would ask interview questions that would be answered with snippets from the artists’ music. I’m a huge Will Oldham fan, but found this rare and out of print collectors item a complete piece of uninteresting crap! I thought I was getting real interviews on vinyl.
I just bought one called * Convention '72* by th Deligates on 45 at a record store for ten cents. I love these things, I wish I could find more.
I remember these, particularly the one with ET. I’m not old enough to have heard the one about Nixon, and my parents didn’t listen to a radio station that would have played the Jaws piece.
That said, I’ve made one of these about Michael Jackson, and they’re not at all easy to do. Song clips are a pain to edit digitally; doing it on tape had to be a lot harder. Working with brief snippets has the potential to get messy. Writing questions to fit the clips isn’t that difficult, but the context has to be understood and the question has to match the clip 100%.
I’m pleased to say that most people who have heard my piece have liked it, but it cost me an award because of the rather low taste level. 
Anyone who wants to hear it is welcome to PM me with an e-mail address.
Robin