Now you can get some more statistics for your YouTube videos, with the recently launched Insight tool, available in your YouTube account (under Manage my Videos, which is probably temporary). The new stats feature is described like this by Tracy Chan, YouTube product manager:

For example, uploaders can see how often their videos are viewed in different geographic regions, as well as how popular they are relative to all videos in that market over a given period of time. You can also delve deeper into the lifecycle of your videos, like how long it takes for a video to become popular, and what happens to video views as popularity peaks.

Darren over at ProBlogger takes a closer look, with a bunch of screenshots detailing some stats for his videos.