The ShortURL plugin provides short canonical permalinks to your posts and pages similarly to WordPress.com via its WP.me service.

kanedo

Pretty ShortURLs

Generates pretty shorturls (without GET Params)

akrabat

Shorter Links

Override the default WordPress "shortlink" URL with one that has a custom text in it. You can also set a different base URL.

whomwah

RevCanonical

A Wordpress plugin that creates and adds support for shortened urls plus the shortlink auto-discovery tag

Nikolay Kolev

The ShortURL plugin allows you to use your blog as your own URL shorterning service by implementing the <a href="http://wiki.snaplog.com/short_url" rel="nofollow ugc">Short URL Auto-Discovery</a> specification. Your short URLs will be in the form of <code>http://domain/-code</code>.
The auto-discovery feature allows third-party services that honor it to use your own short URLs instead of generating new ones using services such as <a href="http://tinyurl.com/" rel="nofollow ugc">TinyURL</a>, <a href="http://bit.ly/" rel="nofollow ugc">bit.ly</a>, and others. This gives your posts and pages canonical short URLs that give you all SEO benefits and don’t leak traffic out to external domains and will prevent linkrot. The homepage short URLs is set to just <code>http://domain/</code> as a unique feature.
The other great benefit of the ShortURL plugin is that the generated short URLs won’t break if you change the permalink structure of your blog or rename the slug of a particular post or page.
Due to the recent choice of both the <a href="http://microformats.org/" rel="nofollow ugc">Microformats</a> community and <a href="http://wordpress.com/" rel="nofollow ugc">WordPress.com</a> to use <code>rel="shortlink"</code> vs the alternative proposals, the ShortURL plugin is also using it now.
More on the topic:
<ul>
<li><a href="http://microformats.org/wiki/rel-shortlink" rel="nofollow ugc">Microformats Wiki: rel=”shortlink”</a></li>
<li><a href="http://en.blog.wordpress.com/2009/08/14/shorten/" rel="nofollow ugc">WP.me – shorten your links</a></li>
</ul>
<h3>To Do</h3>
<ul>
<li>Test against <a href="https://wordpress.org/" rel="ugc">WordPress</a> 2.9 and <a href="https://mu.wordpress.org/" rel="nofollow ugc">WordPress MU</a></li>
<li>Add a settings page</li>
<li>Add a widget</li>
<li>Integrated with <a href="http://www.google.com/analytics/" rel="nofollow ugc">Google Analytics</a></li>
<li>Integrate with the top <a href="http://twitter.com/" rel="nofollow ugc">Twitter</a> plugins to use ShortURL instead of third-party services</li>
</ul>

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