As part of an Audiobook Week discussion, hosted by Devourer of Books, here's a MY list of recommended audiobooks. It's almost more difficult to recommend audiobooks than regular books because you have to recommend both the story and the narrator.
For someone new to audiobooks, I definitely think the Harry Potter series is a good place to start. I've only heard the Jim Dale versions but have heard good things about the Stephen Fry versions as well. I'd also suggest they visit a site like Audible.com which allows listeners to preview books--important to make sure the narration isn't going to drive you crazy.
For me, the fiction books that lend themselves to audio format are the ones told in the first person. Because it seems like they are telling you a story rather than some other person reading a book to you.
The Amelia Peabody series by Elizabeth Peters, narrated by Barbara Rosenblat, is probably my favorite series. Rosenblat does a terrific job with the accents and difficult Arabic words. You never have to wonder who is talking because they sound unique. German, British, American, Egyptian...she masters them all.
I also really like the Aisling Grey, Guardian series by Katie MacAlister (also narrated by Rosenblat), the Tempe Brennan series by Kathy Reichs (again, narrated by Barbara Rosenblat)--noticing a theme?-- and the Black Dagger Brotherhood series by JR Ward narrated by Jim Frangione.
My husband really likes the Dark Tower series by Stephen King, the Stephanie Plum series by Janet Evanovich, and the Incarnations of Immortality series by Piers Anthony. He can't stand the Amelia Peabody series, though, and that seems to be a consensus among most male audiobook listeners I've asked.