How do I switch off the Project Paint mode? The Project Paint mode is on by default and it seems there is no way to turn it off for painting around corners without projection.
It's no longer possible to disable Project Paint mode - the option was removed as of version 2.67. Specifically:
Disabling projection mode is no longer possible in 3d viewport. This was exactly equivalent to simply painting in the image editor, so it was removed as part of the painting code refactoring.
However, this really isn't such a bad thing. The best option, as far as I'm aware, is to enable Face Selection Masking for Painting while in Texture Paint mode.
With this enabled, you can now right-click on each face of your model (or Shift+RMB for multiple faces) to limit your brush strokes to those surfaces only.
Similarly, you can also use selection tools that would typically be available elsewhere, such as Circle select (C), Box select (B), or Select Linked via L while hovering mouse cursor over a surface to select the entire UV island with one button.
Whichever way you do it, your brush strokes will be limited to the selected faces.
The one downside is that this won't immediately give you the performance boost you might have appreciated by disabling Project Paint mode in the past - but hopefully that'll prove to be less and less of an issue as Blender continues to be optimized and hardware gets more powerful.