I find myself recommending the same systems over and over and over. Whether out of my familiarity with a system, its described usefulness, or just its popularity, some systems just stand out as good choices.
So below are what I recommend for different tasks. These systems can be used as a starting point in your search or research.
For more specific recommendations, please post a new topic in the forum.
Blogs
WordPress, Serendipity
Community Site
Drupal, PostNuke, Xoops
Content Management (general)
Drupal, Joomla, WordPress, MODx
Newspaper, Magazine, or Article Site
Drupal, WordPress, MODx
Podcasting
LoudBlog, WordPress
Photo Gallery
Gallery, ZenPhoto, Plogger