The winner here, by far is Amazon.com. Their database is enormous and well arranged. If you know what you want, you can find it in an instant, by title (or partial title), composer, or artist. If you're not sure, there are extensive browsing mechanisms in all classical categories. The entry for each CD is crammed with details. The album cover is displayed. For most CDs, you can even listen to samples -- a great way of getting a taste of unfamiliar music or of deciding among performances. Useful reviews (some by professional critics, some by amateurs) are often included, as are recommendations, lists, and references to other CDs that may interest you. Ordering is a breeze; customer service is prompt and courteous.
It may come as a surprise to some collectors, but there are a lot of first-rate classical CDs (including ones by the major labels) that are not directly available in the US. If you can't find what you want at amazon.com, you'd be wise to try their affiliates in England (www.amazon.co.uk), France (www.amazon.fr), and Germany (www.amazon.de). Even if you don't know French or German, patience and imagination (and maybe a dictionary) should enable you to negotiate the foreign-language sites, which have exactly the same format as the American Amazon.com. (For the valuable Japanese Amazon -- (For the valuable Japanese Amazon -- www.amazon.co.jp -- you do have to know the language, since the whole site is in Japanese script.