Asana - Easy for non-technical folks to grok, all the features I need for non-coding projects (like a marketing project for example)
Pivotal Tracker - More technical features specifically for software development, steeper learning curve, good bug tracking.
Slack - Good for office-wide communication. Easy to use for everbody.
Bugherd - Bug tracking system which integrates into the user-facing components of your web-app. Makes gathering feedback/bug-reports from the public very easy.