it's much more natural to say "I am taller than him". Although, perhaps in very old English people may say "taller than he". But this sounds very strange to the native ear. I hope this helps ! : )

I was taught in school that the correct grammar here is "I am taller than he". The full, correct sentence (again, according to grammar books) is "I am taller than he is." Because "he" is the subject that goes with the verb "is" you wouldn't use the object pronoun "him." Even if you don't use the final "is", it's still implied. That said, Thom is absolutely correct -- nobody I know says it in natural conversation. There are people who still think it's really important, though.

I think I was taught that the only correct way is "I am taller than is he". I still remember the sentence my teacher wrote "He runs faster than do I"; I read a similar sentence in my architectural textbook lately so I guess this might be an extremely formal way. (Someone correct me if I'm wrong.) But anyways, I myself say "I am taller than him".