How can I make the terminal window close automatically on OS X?

Go to Terminal -> Preferences, then on the right hand side select "Shell", then select "Close if the shell exited cleanly" from the dropdown labeled "When the shell exits".

This will close the shell if it exited without a problem (such as when you typed "exit"), but if the process returns an error it will stick around so that you can see what it was.

Additionally, you can execute the following command (or add it to the end of your .sh shell script) in order to kill the Terminal application:

kill `ps -A | grep -w Terminal.app | grep -v grep | awk '{print $1}'`