I only like listening to audiobooks as a 're-read' given a good narrator. When picking up a book for the first time, I need to actually read it.
What I generally like to listen to are lecture series...on history, on science & technology, on psychology and economics, etc. Most of these I find available for free on Youtube - there are plenty of university channels (including Yale university) that upload entire courses worth of lectures. So, I just download those and convert them into mp3 files. There are also a huge number of lectures available through The Great Courses or The Teaching Company on basically any topic you can think of, and they're pretty much all of an extremely high quality and standard.
Some audiobooks that I think are generally great:
Patrick O'Brian's Aubrey-Maturin series narrated by Patrick Tull. Excellent historical naval fiction. Tull is probably one of the best narrators I've ever come across. He completely embodies his characters, does excellent accents, and whenever occasional excerpts of poems or songs appear, he recites with real musicality or actually sings, and sings well! His intonation, his tempo, his tone, even his mirth...it's all just perfect.
Some of Jane Austen's novels. There are so many narrators for her books, and the majority of them are not good. A few are gems. My favourites are Prunella Scales narrating Emma, Anna Masey narrating Persuasion. Unsurprisingly, Pride and Prejudice has the most number of narrators because of its popularity, but they are surprisingly some of the worst. I really dislike them all. The only one I found to be good after extensive searching was a narration by Irene Sutcliffe, but she has a decidedly older and more patrician sounding voice. There is a new narration out by the actress Rosamund Pike, and I heard bits of it and think it's actually quite decent, but nowhere near as excellent as Prunella Scales or Anna Masey. Prunella Scales, like Patrick Tull, embodies her characters in Emma and completely changes her personality through her voice. She is brilliant, especially regarding one chatter-box of a character who just can't stop speaking. I was bloody impressed by Scales - how she could make such long speeches in just one breath, and so fast, and with such comic effect...
I also recommend a science fiction audiobook: Iain M. Banks' The Player of Games narrated by Peter Kenny. A wonderful book, and a perfect introduction to Banks' Culture milieu. It's divided into 3 or 4 sections, and if you remove the science fiction signifiers, the first section almost reads like a realist novel. But it is unabashedly SF, full of high-concepts and wit, and is an adventure tour de force that is centred around a game. It's one of those books that explores the theme of "game as life" in all its social, political and personal aspects.
If you like learning about history or literature or whatever else, look into The Teaching Company or The Great Courses. They have introductory lecture series, each lecture about 30 minutes long, and they are far from boring.