Interestingly enough, ancient Greek [1] did happen to be tonal even though modern Greek is not. More specifically, it had had pitch accent [2] which is somewhat different than fully tonal languages like Chinese but more involved than languages like English which have stress accent.
Ah, yes. The pronunciation changed over the years and nobody in recent memory can remember when Greek was tonal (I'm not entirely sure when this was), but we got rid of it about 60 years ago? My dad can remember writing in polytonic, but it didn't make any difference to pronunciation by then.
[1] http://en.wikipedia.org/wiki/Polytonic_Greek
[2] http://en.wikipedia.org/wiki/Pitch_accent