The hash (#) and star (*) or asterisk keys in mobile phones were included only to adjust the number son the keypad. As you have noticed there are 10 numbers in the keypad divided in group of threes, after which 0 remained alone so they added a star and a hash to make it a pair of 3.
But with the passage of time short keys were introduced to make tasks easy on mobile phones, as the star and hash were on the keypad they become the main source of codes and keys and you hardly find any short code without using them.
Just think any code or key and see how they start and end on these keys. Whether you want to activate a message package, want to get a ringtone or want to start your 3G bundle you have to use these buttons.