I don't know why I hadn't heard about AppShopper before. A friend sent me a link, and my initial impression is that it's one of the best websites for searching for apps. It has a number of useful features that the App Store lacks. The site seems to be a compendium of the content in the App Store. But unlike the App Store (and please correct me if I'm wrong), when you do a search, you can sort the results.
For example, if you're interested in astrology apps, if you search on "astrology" in the App Store, you get a page that lists apps, podcasts, songs, etc., related to the topic. Click on See All in the truncated apps results, and you'll get a page filled with astrology-related app icons in no particular order.
But if you do a similar search on AppShopper, you can sort the results by broad category (the App Store categories of Books, Business, etc.), relevance, price, update, and rating. The site also gives you many other views of the App Store, including popular, paid, free, updates, new, and price changes. You can use these views to look at the App Store by category or as a whole. In short, this site gives you just about any angle you want to get a handle on the 150,000 apps available. PLUS, you can get a range of RSS feeds, such as the most popular new apps, or the most popular new apps that are free.