The Master and Margarita by Mikhail Bulgakov is possibly my favourite magical realism book. I found that some of David Mitchell's writing is similar to Murakami, specifically number9dream, Ghostwritten and Cloud Atlas. Through reading Murakami I've gotten into Kobo Abe, he shares that weirdness with him and are very Kafkaesque, I loved The Woman in the Dunes and The Box Man.

The Master and Margarita and Wind Up Bird Chronicle are two of my favorite books at the moment, so this seems like a good bet. The way both authors blend physically/spatially/temporally distinct characters and settings into one narrative is very similar, and incredibly satisfying.

Salman Rushdie all the way!

My favorite is satanic verses, by far.

Midnight's children is his most popular work though.

For both books, having even a basic knowledge of Indian history would make the experience much better.

The ground beneath her feet is incredible too. Shame is intense, and if you're feeling thin on South Asian history I'd go with either.

Or if you want to go with European/world history, enchantress of Florence is a good one. Very well reviewed but I personally never read beyond the first thirty pages.

His new book 1001 nights is coming out this Sept. The short excerpt published in new yorker from it was incredible, so that might be a good option too.

East/West is a great short story collection, but has less magic than his novels.

Great suggestions, thank you very much (and the same holds for the other replies to my question).

If you like magical realism, you might enjoy One Hundred Years of Solitude by Gabriel Garcia Marquez. It is a metaphoric interpretation of Columbian history based upon the lives of many generations of one family.

I loved it (it took a few attempts to finish it though).

I think Marquez's work is more realistic (and not always evident when he strays into the magical); Murakami sometimes crosses straight into fantasy. If that makes sense at all.

Borges short stories - some of my favourites are very accessible: The Garden of Forking Paths and The Aleph. Some of his stories are difficult to read and make more sense as you know the author better. He wrote interesting works such as reviews on fictitious books. If you are looking for 'not shallow', he's your man. I also second 'The Master and Margarita' recommended by iambatman.

Interesting, I've only read 'Kafka on the Shore' and haven't read another Murakami because I didn't connect with it at all. Maybe I should try 'The Wind-up Bird Chronicle'?

Definitely try 'The Wind-up Bird Chronicle', I think it is regarded as one of his best works although it is a bit slower paced.

For me 'Kafka on the Shore' contained a bit too many magical events that were then left unexplained and unexplored- but I didn't think it was bad at all.

The other novel I really liked was the 1Q84 trilogy.

I would start with Wild Sheep Chase (an unusual quest/adventure story) or Hard Boiled Wonderland (a bit of Lovecraft meets P.K. Dick). Wind-up Bird is slower, a bit graphic and less fun.

Norwegian Wood was my favorite.

As other have said, read Mikhail Bulgakov, including his "Heart of a Dog".

Also try Italo Calvino, his short stories are especially good. Calvino writes in many different literary styles, and magical realism is often at the core of his stories. "The Baron In The Trees" was one of the first books I read by him.

For when you have the mental space, a rather interesting / meta Calvino book: If on a Winter's Night a Traveler

Stick with Murakami, he's pretty much absorbed the entire Western canon and now left us with his charming "shuffling" of it. Hopefully you also read Hear the Wind Sing and Pinball 1973. They were his first two and recently reprinted ( this month, August 2015 ) in English.

I really liked "The Wind-Up Bird Chronicle" too.