File -> Open Recent -> Clear List
However as far as I found, There is no way to remove individual projects from the UI.
We need to find the other.xml file:
- On Windows 7: C:\Users\<username>\.IntelliJIdea12\config\options\other.xml
- On Mac OS, the full path of this file is /Users/<username>/Library/Preferences/IntelliJIdea12/options/other.xml
Then manually edit the list of recent projects inside the XML under
<component name="RecentProjectsManager"> node.