Which module to pick?
No new URL shortening features will be accepted into this module: consider this a backport of the Drupal 7 shortlink functionality. For a module with more flexibility, please look at the Short URL module.
ShortURL is the module with all the features and this one the one without any configuration!
Drupal 7 port
This module will not be ported to Drupal 7, because Drupal 7 already includes support for the shortlink standard. You will only need to install the Global Redirect module to automatically redirect the user to the corresponding alias.
This module offers simple support for the shortlink standard, currently only for nodes.
Typically, you use the Pathauto module to automatically generate path aliases for the content (nodes) you create (or maybe you enter aliases manually). These are typically longer than the original "node/" paths.
This module aims to be independent from other web services and thus uses those "node/" paths for short URLs. This of course implies that your short URLs will only go offline if your site goes offline. This module relies on the Global Redirect module to perform the redirects to the aliased paths.
Note: the shortlink specification seems to have the best chance of ending up being the winner, as WordPress.com (with millions of blogs) has started supporting this standard.
Live sites using this module
(This module was written in less than 10 minutes.)