THE QUICK TAKE: Logitech makes very good speakers, in terms of build quality and sound quality, for their price point. So the key things to keep in mind are (1) make sure you understand what type of speaker system you need, and (2) keep an eye on the price of the options you're looking at. At a discount, these are a reasonably good choice for someone looking for moderately good sound in a fairly compact package.
UNDERSTANDING YOUR NEEDS: No tiny 2.0 speaker system is going to give you a lot of bass, so this entire class of speaker is something of a trade-off of sound quality and space. If you're looking for bass, consider a 2.1 system with a subwoofer / bass extension speaker. The Logitech Z523 Speaker System and the Logitech Z623 Speaker System are examples.
Or, if you want to stick with 2.0, you can move up in price and size to something like the Audioengine 2 or the M-Audio AV-40. At the list price for these Logitech speakers, those systems are their competition, and the Z520 just doesn't match up.
PHYSICAL DESIGN AND FEATURES: In my opinion the Logitech designs are much more attractive than some of the recent Altec Lansing designs (their main competition). The backward angle of the face also adds an important enhancement to sound quality - the speaker cones, especially the tweeters, only perform as intended when they are aimed toward your ears. (That's why lots of users of the box-shaped, monitor-style speakers mentioned above angle the speakers toward them, and add wedge shaped inserts underneath.) Be sure to experiment with what sounds best to you - "toe-in" the speakers by aiming them toward where you are sitting.
The cabinets are large enough (9.1 inches tall, 4.8 inches wide, and 6.5 inches deep) to give better sound than many small speaker systems - the size of the enclosure is a very important factor in speaker performance. But it's unfortunately not large enough, especially given the inefficient shape, to really compete with some of the more serious speaker systems mentioned above. Still, if you get them and think they're a bit bigger than you expected - just realize that's part of what's giving you better quality sound.
Logitech states that the system has 26 watts of total power, which is quite a bit better than most small 2.0 speaker systems and will help to provide undistorted sound. (It won't reach what most people would think of as "party" levels of sound, though.) On power, the Z520 speakers compare fairly well with the other 2.0 systems from Audioengine and M-Audio.
DON'T EXPECT MUCH FROM THE OMNIDIRECTIONAL FEATURE: I really don't understand what Logitech had in mind with the rear-firing tweeter on these speakers. Perhaps they're just trying to find some selling point in a competitive product niche. But sonically it doesn't make much sense given the way it's designed and built. It's too small to add much in a large room, and it's not going to help (and it may hinder) for the way most people place these.