I am a huge fan of American Scientist. Here are my reasons:
1) Broad subject matter. From physics to engineering to biology to statistics to mathematics and more.
2) Well written articles. American Scientist, to me, perfectly navigates the waters between the vapid dumbed down nonsense in most popular science magazines, and the dryness of a full publication. Their articles can be challenging, but are rarely dull.
3) Articles often add an element of humanity to the picture - what kind of people were involved in this research? What real problems occurred? Often the articles are willing to discuss the contact between the science and society, and not in the pathetic "omg this will make your lives great" way most magazines do.
4) American Scientist publishes well written articles critical of established scientific culture. Six years before most media even considered being critical of string theory, Peter Woit was published in American Scientist (2001). While the rest of the science-for-the-public zines are worshiping Einstein, AS actually published an article critical of the way he is perceived. The book reviews are also excellent, often being so informative as to really deserve the word "article" themselves. As you can tell, this reason above all others is the one that endears this magazine to me. I do not believe they are harsh or aggressive - AS is just willing to take a hard look at sacred cows.
Some downsides to AS:
1) Comes out every other month. The issues provide a great deal of reading, but I usually bang it out in less than 30 days, leaving me a whole month to wait for the next!
2) When I said it had a diverse range of articles, I meant it! I consider being informed on many areas of science important, but there has been an issue or two that just didn't interest me.
However, unlike Science and Nature, AS is actually affordable.
Highly recommended.