Alexa Rank is a ranking system which bases its ranking schema on the level of traffic each website receives from the number of people who visit a website with the Alexa toolbar installed.
It is important to increase Alexa rank because advertisers and advertising services use site’s Alexa rank as a way to determine the worth of a link and the popularity of the web site.

Why would you want to improve Alexa ranking?
•    It makes you feel good and gives you bragging rights.
•    More importantly it means that your site is popular, which creates a viral effect.

There are two easy ways to start using Alexa. If you are using Internet Explorer, install the Alexa Toolbar. If you’re using Firefox, download the SearchStatus extension which displays the Alexa Rank, Google PageRank as well as other useful features. I highly recommend that you use Firefox and SearchStatus instead of Alexa toolbar, which I find to be more bulky and less useful.

To increase your Alexa rank in the long run, I would highly recommended that one focus on developing quality content which attracts and maintains a large audience instead of purely focusing on artificially increasing your Alexa Rank.
Besides that, I tried to search few more points of how to increase Alexa ranking, which I have pointed below-

1.    Install the Alexa toolbar or Firefox’s SearchStatus extension and set your blog as your homepage. This is the most basic step.
2.    Put up an Alexa rank widget on your website. I did this a few days ago and receive a fair amount of clicks every day. According to some, each click counts as a visit even if the toolbar is not used by the visitor.
3.    Encourage others to use the Alexa toolbar. This includes friends, fellow webmasters as well as site visitors/blog readers. Be sure to link to Alexa’s full explanation of their toolbar and tracking system so your readers know what installing the toolbar or extension entails.
4.    Get friends to review and rate your Alexa website profile. Not entirely sure of its impact on rankings but it might help in some way.
5.    Write or Blog about Alexa. Webmaster and bloggers love to hear about ways to increase their Alexa rank. They’ll link to you and send you targeted traffic (i.e. visitors with the toolbar already installed). This gradually has effects on your Alexa ranking.
6.    Write content that is related to webmasters. This can fall in the category of domaining and SEO, two fields in which most webmasters will have the Alexa toolbar installed. Promote your content on social networking websites and webmaster forums.
7.    Make sure your site is active on Twitter, Facebook, Digg, Delicious and StumbleUpon.
8.    Create a webmaster tools section on your website. This is a magnet for webmasters who will often revisit your website to gain access to the tools. Aaron Wall’s webpage on SEOTools is a very good example.
9.    Use PayperClick Campaigns. Buying advertisements on search engines such as Google or Exact Seek will help bring in Traffic. Doubly useful when your ad is highly relevant to webmasters.
10.    Post in Asian social networking websites or forums. Some webmasters have suggested that East Asian web users are big Alexa toolbar fans, judging by the presence of several Asia-based websites in the Alexa Top 500. I suggest trying this only if you have the time or capacity to do so.
11.    Get Dugg or Stumbled. This usually brings massive numbers of visitors to your website and the sheer amount will have a positive impact on your Alexa Rank. Naturally, you’ll need to develop link worthy material.
12.    Buy banners and links for traffic from webmaster forums and websites. A prominent and well displayed ad will drive lots of webmaster traffic to your website, which can significantly boost your rank.
13.    Hire forum posters to pimp your website. Either buy signatures in webmaster forums or promote specific articles or material in your website on a regular basis. You can easily find posters for hire in Digital Point and other webmaster forums.
14.    Pay Cybercafe owners to install the Alexa toolbar and set your website as the homepage for all their computers. This might be difficult to arrange and isn’t really a viable solution for most. I’m keeping this one in because some have suggested that it does work.
15.    Flaunt your URL in webmaster forums. Webmasters usually have the toolbar installed. You’ll get webmasters to visit your website and offer useful feedback. It’s also a good way to give back to the community if you have useful articles to share with others.
16.    Don’t forget, more traffic = better!

There are few useless tricks I will like to mention that does not help increasing Alexa ranking very much.

1. Installing Firefox Extension That Reloads Web Pages
The extension for Firefox named ReloadEvery reloads web pages at a certain time period on user’s direction. I’ve found many people were using this to increase their page views, hopefully thinking Alexa would count towards their Alexa ranking. Unfortunately, this doesn’t work at all because multiple requests for the same URL on the same day by the same user counted as a single pageview by Alexa. And if you’re using Google Adsense, consider your account to be banned!
2. Install Alexa Redirect Plugin for WordPress
Installing Alexa Redirect Plugin for WordPress will edit all your internal blog links to add the “Alexa redirect” prefix, i.e., http://redirect.alexa.com/redirect?
However, let me tell you one thing, this doesn’t work on persons who does not have Alexa toolbar installed. Far worse than that, it will completely destroy your internal linking structure of the site. In addition, there is no solid proof that using such will increase Alexa’s traffic ranking.
3. Install Alexa Toolbar on Several Computers in Your Local Area Network and Set Your Site as Your Homepage. Perhaps it will be useful to note that this may work only when dynamic or different IPs are used.
4. Using an Alexa Auto Surf
Alexa auto surfs may work for new sites with terribly low Alexa ranking, but it seems as soon as Alexa discovers people using Auto Surf programs, the website ranking will cease to improve! In addition, if you’re using google adsense, you may get into trouble!

Some random Alexa rankings:
Google: 1
Facebook: 2
Twitter: 14
eBay: 25
CNN: 60
Digg: 104
See what is Alexa rank of your site? http://www.alexa.com/

What do you think of Alexa? Have you tried increasing your Alexa Rank by any of these methods?

Sources:

http://www.doshdosh.com/20-quick-ways-to-increase-your-alexa-rank/
http://www.johntp.com/2007/04/12/how-to-increase-alexa-rank/
http://www.enfotainer.com/2008/08/4-useless-tricks-people-use-to-increase-alexa-rank/
http://ben-lang.com/10-free-ways-to-improve-your-alexa/

Photo Credit:

http://www.entrepreneurs-journey.com/549/how-does-alexarank-work/