Why is my site broken after upgrading

From Joomla! Documentation

In Joomla 1.5.16 & 1.5.17 there is a feature that checks plugins for errors. http://joomlacode.org/gf/project/joomla/tracker/?action=TrackerItemEdit&tracker_item_id=19859

If a plugin causes some error, it gets unpublished. But a certain plugin might give an error during the actual upgrade (because the file hasn't been copied fully via ftp yet) or during a server hickup. This can cause the unpublishing of vital plugins (like the SEF plugin).

So the solution is to go into your Plugin Manager and republish the plugins that need to be published. If some plugins are unpublish that cause you to not be able to login to your administrator, you can republish the necessary plugins via your database manager (like phpMyAdmin). Only do that if you know what you are doing...

PS: Of course it is advised to always make a backup of your site (files and database) before upgrading. And to set your site to Offline Mode (via Global Configuration) during the actual upgrade.