How do I Install GTK+ 3.0?

To use gtk2 or gtk3 apps you don't need to install anything. But, if you want to develop (or even just compile) apps this is what you're looking for:

sudo apt-get install libgtk-3-dev

GTK3 is installed by default, please don't download and compile from the GTK website.

If you want to use GTK3 yourself, compile against that instead GTK2, or use PyGObject instead of PyGTK if you're using Python.

If you want all programs to use GTK3 instead of GTK2, it won't work, it's a job for the application developers to port their application.