I don't know about you guys, but I've been loving my Google toolbar too much to even remember using my old Alexa bar. In fact, I see great sites with Alexa numbers dropping like flies. (Michael Gray's website for instance) So it is with this I must say that I could care less about any Alexa rank any more!
Of course Alexa isn't the best way to determine a site's popularity but it is still used by a lot of people to do just that. Enough people have the Alexa toolbar installed for it to make a difference, and also there is the fact that it is an extremely well known website, especially in its niche. If Alexa could come up with a better way to gain internet metrics then they could improve their credibility.
Alexa changed their algorithm of ranking the websites some time back, and now its functioning a bit better. Whatever you say, i have noticed that rather than direct/returning traffic, search engine traffic is taken into consideration. They have not said that, but checking my blog stats and comparing with the changes in alexa ranking, showed this.
Actually I don't really bother much about Alexa. It's not that accurate anyway because it only takes into account the number of users having Alexa toolbar that visited your site.
Its just a tool to be used in conjunction with other tools. Its not the most accurate and only gives figures of a specific type of user, but it is useful when used as part of a tool subset.