According to the strict rules of harmony, octaves are not harmony. It's just the same note, only higher or lower. A 5th is harmony, but if you do two or more of them in a row (parallel 5ths), the prof will dock you points because all you're doing is having one note ride on the second overtone of another. It's too easy and not very creative. Practically, it can sound pretty good, though. Same situation with parallel 4ths, because 4ths and 5ths are inversions of each other.
You can do parallel 3rds and 6ths 'til hell freezes over and it sounds great, but it can get a bit cloying after a bit. It helps for the voices to go in opposite directions from time to time rather than doing everything parallel.