In brief: this is a plugin that provides a tempalte function to pull a user-specified number of links from the WP Link Manager and display them in a format of your choice, or, if you prefer, just return them as a nice big associative array. I've seen plugins that do similar "random link" things, but they relied on external files. This uses all the links you've lovingly stored in Link Manager, which makes more sense to me.
Anyhow, you can get the plugin and full documentation here:
Hope you find it useful. Feedback is welcome.