When trying to access Organization tab on My Profile page in SharePoint 2010 My Site, the Organization Browser Silverlight control partly loads, but soon freezes the browser, and consumes all available CPU (well, on multi-core CPUs only one core, to be exact). Only option is to kill browser process and stay away from the Organization Silverlight.
When looking at the HTTP traffic using Fiddler, I noticed that page Silverlight control loading seemed to halt more or less immediately after querying information of a same specific individual using /MY/_vti_bin/SilverlightProfileService.json/GetUserSLProfileData.
So, I went to the profile of this user and found out that if a person is a Manager of himself/herself, the Silverlight control will crash. It is probably going into some never-ending loop. In my case the problematic user was the most top-level manager. After I modified the profile of this user in Central Admin and cleared the manager field, Organization control started working.