Shel Silverstein was notorious for not giving interviews, stressed in the 1975 interview with Publisher's weekly: "...and I'm not going to give any more interviews." This sentiment was brought up again and again in the obituaries, as well as during the heyday of A Light in the Attic, when Ed McDowell of the New York Times Book Review wrote an entire article in praise of the work, but admitted that he'd hadn't tried to contact Silverstein in light of the attitude towards interviews.
As it turns out, while Shel wasn't exactly going to give interviews left and right to just anyone, there are interviews post-1975. I have a select few, though a couple of others are forthcoming. As well, if I can ever track it down (or a transcript) I would dearly love to include the 1994 interview (on CD) of Silverstein and Bob Gibson conducted by Studs Turkel. And there are plenty of offerings from the 60s and 70s that I am sure are just waiting to be included.
The Aardvark Interview from 1963, it is, by far, the most in-depth interview Silverstein ever gave. Definitely a must-read and a treat.
An interview from 1965, from the album "I'm So Good That I Don't Have to Brag." Is it a real interview, or is it bogus? I suggest you decide--because even now, I'm not so sure...
Chicago Tribune interview from March 4, 1973. Talks mostly about the then-current album "Freakin' at the Freakers Ball," but there's lots of other good stuff tossed in here, too.
Publisher's Weekly interviews Shel Silverstein: February 24, 1975. Because of his proclamation that he would be "giving no more interviews", this one tends to be quoted often, especially the bits about Shel's childhood.
The Third Mr. Silverstein: New York Times, April 30, 1978. Not an interview; more like a conversation.
The Stars and Stripes 50th Anniversary Edition Issue from 1995 has a retrospective on Shel, with excerpts from an earlier interview from 1969.
The Old Dogs site has a full-length article about the making of the album, a special project involving Silverstein, Waylon Jennings, Mel Tillis, Bobby Bare, and Jerry Reed. It's not an interview per se, but it does have quoted comments from Shel which are rather amusing. Patsi Bale Cox put together the liner notes in late 1997.