Anathem is a big, think, dense book. There's no getting around it, so I'll just open with that. It's around a thousand pages long, thick enough to serve to reach the pack of the high shelf in your kitchen, and dense enough that you could pass it off as "intellectual" if you're feeling self-conscious about all the science fiction you've been reading. Don't let it intimidate you! This one is worth settling down with for the long haul and giving a good mulling-over. Don't worry, I'll try not to borrow Stephenson's loquaciousness for this review.
The first fifty pages or so were difficult for me. Not because of the denseness of the text, but because I thought Stephenson was trying to pull one over on me. The story takes place in a medieval-feeling monastery on an alien world, though we quickly learn that the world outside the monastery walls is more technologically advanced than the cloistered world within them. As the narrator, a monk named Erasmus, introduces us to life in the monastery we are necessarily introduced to the philosophy of the people who founded it. I've got a solid background in philosophy, so I immediately picked out the elements of Plato, Thales, and other early greek thinkers. However, they were presented with slightly different metaphors, new names, tweaked personal histories. I really thought for a time that Stephenson was trying to pull one over on me, trying to pass off the works of great historical thinkers as his own!
Fortunately, I kept reading. Before long, it occurred to me that rather than trying to co-opt the philosophers ideas, Stephenson was writing a primer on ancient thought and philosophical advances across the centuries, but couching it all in a fascinating new setting and some science fiction. Clever! I settled down to enjoy myself. It was only much, much later that I realized what Stephenson was *really* doing, and by then I was already completely sold on the book both as a narrative and a source of interesting ideas. I won't spoil it for you any further, I'll only say: give it some time. If you don't know any philosophy, enjoy discovering it in an interesting way! If you do, you'll have fun seeing what he did with it.
So, that was my complaint with the book. I've heard another from a friend who didn't give it enough time: too much unnecessary new vocabulary. Yes, there are new words for simple things. Truck, phone, student, TV, monastery. These all get new words, and I can see where a casual reader would get frustrated having to learn vocabulary just to understand the story. It's a valid complaint, but you'll quickly become used to it (he's good at defining with context) and stop paying attention to it at all once you settle in... and there *are* good reasons for it. Partly it's just to emphasize that the culture you're reading about isn't of Earth. The rest I'll let you discover, but I have to emphasize this again: this is a book that you need to really invest some time and mental energy towards, not some throw-away space opera yarn.
Complaints out of the way, I loved this book! It was crammed with fascinating ideas from the very old (like Plato) to the very new (like quantum mechanics). The story that plays out on top of these ideas (I assure you, it's not the other way around) is well told, interesting, and occasionally completely gripping. The world is deep and fascinating, and I'm more than a little sad that I have to stop half-living in it now. The characters tend towards the flat, and there are times when it's easy to lose track of who a particular name corresponds to. There are exceptions to this, of course, and it's not nearly bad enough to be a show-stopper, just a weakness.
So, bottom line: I highly recommend this book. Next time you're feeling like you need something a little meaty, pick it up and make sure to give it some time to ramp up. You'll be well rewarded, both narratively and intellectually.
 In the acknowledgements, Stephenson mentions that the conceit of the book prohibited footnotes. That said, he created a truly excellent online reference for the sources of the idea seen in the book: http://nealstephenson.com/anathem/acknow.htm. Bravo.