You'd think that as soon as Harry met someone who was friends with his dad, he'd have asked about his family. Certainly Lupin or Sirius could have told him something of his family, given that they were James' closest friends, and Sirius was "always welcome at the Potters". Obviously there's nothing in the books, but did J.K. Rowling ever explain why there was no mention of any living relative other than Aunt Petunia, or even what happened to Harry's grandparents?
Yes, she did.
Petunia is Lily's only sibling. Lily and Petunia's parents died of natural causes before Harry and Dudley were born.
James Potter was the only child of his parents, who were slightly older. James' parents also died of natural causes prior to Harry's birth.
JK Rowling has said that she makes no mention of them in the books because they have nothing to do with the story. She purposefully had to have Petunia be the only available relative for Harry for plot reasons.
MA: What about Harry's family — his grandparents — were they killed?
JKR: No. This takes us into more mundane territory. As a writer, it was more interesting, plot-wise, if Harry was completely alone. So I rather ruthlessly disposed of his entire family apart from Aunt Petunia. I mean, James and Lily are massively important to the plot, of course, but the grandparents? No. And, because I do like my backstory: Petunia and Lily's parents, normal Muggle death. James's parents were elderly, were getting on a little when he was born, which explains the only child, very pampered, had-him-late-in-life-so-he's-an-extra-treasure, as often happens, I think. They were old in wizarding terms, and they died. They succumbed to a wizarding illness. That's as far as it goes. There's nothing serious or sinister about those deaths. I just needed them out of the way so I killed them.
ETA: Because someone might ask, here is a link to the HP Lexicon, my source. This links to the information about Harry's Potter grandparents; the information on his Evans grandparents can be found by clicking on Lily's links as well as the relevant link on Pottermore
Lily's parents were not magical and would have fulfilled the requirements if his mother's blood that was necessary for his protection. I find it odd that his grandparents all could have died of natural causes before his birth, considering that his parents were only 21 when they were killed. This would have only put his grandparents in the 40's to 60's range.