Hugo Taking Dutch Further Course
This course is justly popular; it's out of print but used copies can still be found on Amazon. It starts at a low enough level that someone who has done little more than read a quick primer can follow it, but fairly quickly goes into more sophisticated (and interesting) material, including excerpts from real literature, which are rewarding to read and understand. Best of all, it comes with a set of useful audiotapes. Unlike tapes for tourists, which often involve lots of pat phrases and lists of numbers, these tapes include the excerpts, read aloud, with questions for you to answer aloud. I compiled all the excerpts onto a tape, it was my main source of spoken Dutch for a long time.

Het Achterhuis
This title will be more familiar to you as "Anne Frank's Diary" (the real title is something like "the house behind"). Not only is this readable and interesting, but it's one of the better-known works of Dutch literature, and hence easy to find.

Harry Potter
Ordinarily I'd never advocate trying to learn a language by reading books translated from your own, but in every other respect, these books are very good for learning. They're easy to acquire, easy to follow, decently translated, and present many hundreds of pages of continuous text. I started out with "Harry Potter en de Vuurbeker" (the longest one available at the time, and hence the best value!). At the beginning, since I was trying fiercely to avoid resorting to a dictionary, I was reading a few pages at a time, roughly once a week. After I got through the first 200 pages, I felt a lot more comfortable, and I read the last 150 pages in a single evening. (One downside: these books will fill your head with some amount of totally useless vocabulary. E.g. "spreekskobold" or "spokesgoblin"--I doubt I'll be using that one in future.)

Works by Remco Campert
Campert is an essayist who writes short, funny pieces that have been collected in many volumes (and often feature in Dutch language textbooks). Some are oblique and idiomatic enough to be quite difficult to understand, but others aren't, and it's very rewarding to be able to pick up on the witticisms.

De zon uit Spanje
This is a Dutch bestseller that I happened to get my hands on last winter. It's a family saga told from the point of view of each family member in turn. It starts off a little slow, but gets more and more intriguing as it goes. When I was able to describe the titular son to a friend of mine, in English, as "a busker and itinerant arborist," I knew I'd really learned to read Dutch!