I am taller than he is ---->; CORRECT
I am taller than he --------->; CORRECT
I am taller than him. ------->; WRONG (Though used a lot, but incorrect)
My book is better than yours ------->; CORRECT
My book is better than yours is ----->; NEVER HEARD OF IT
There is a huge explanation for the same. But to cut it short, just think that we are comparing our height to the height of the other person, not TO the other person.
Or simply turn around the sentence and see if it fits.
I am taller than he is
He is taller than I am ---> RIGHT
I am taller than him
him is taller than i am ---> WRONG
It is okay to omit the is at the end since it is understood. Though pure grammar would warrant the use if the ''is'' as well.
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It is still a hotly debated topic, but for now, just understand that the above is correct in FORMAL english :)
See the entire debate here :
http://grammar.quickanddirtytips.com/than-I-versus-than-me.aspx