Content is King. As with all SEO/SEM/traffic-related strategies, your long term goal should focus on developing quality traffic which attracts and maintains a large audience and not artificially increasing your Alexa Rank. Great content = more visitors = better Alexa rank.
Install the Alexa Toolbar or Firefox’s SearchStatus extension and then then surf your own site (note that Alexa will count a user’s visit only 1x per day). Now you can guarantee at least one of your visitors have the Toolbar installed.
If you work in an office or have multiple computers in your home, install the Toolbar on every computer and set each browser’s homepage to your domain. Note that this may work only when dynamic or different IPs are used.
Encourage others to use the Alexa toolbar… co-workers, friends, fellow webmasters as well as site visitors/blog readers.
Try to get your articles on such social bookmarking sites as digg.com, del.icio.us, or stumbleupon, as this can drive high numbers of visitors to your site and the resulting traffic will have a positive impact on your Alexa Rank.
Place an Alexa widget on your Web site. Note: I only recommend displaying your Alexa Rank once it falls below 200,000.
Write high-quality content that appeals to webmasters… e.g. articles on SEO, generating traffic or domaining. Promote this content on webmaster forums and on social networking sites. The idea is to get as many Alexa Toolbar users as possible (read: geeks, webmasters, search engine optimizers & marketers) to visit your site, since there’s a greater probability that they will have the Alexa toolbar installed.
If you’re planning a media buy, considering buying ad space on webmaster forums and websites. Paid advertising can drive great traffic period, but webmasters are more likely to have the Alexa Toolbar installed.
Optimize your site (or relevant pages of it) for Alexa related keywords.
I’ve read in several forums that that Alexa Rankings are widely used in East Asia and that it can be helpful to seed links into Asian social networking forums.