The correct spelling is 'millennium' and it means a period of one thousand years. The word comes from Latin, so the commonly used plural form is 'millennia'. It is quite appropriate to write: '... has changed many times over the millennia'. 'Over the generations' is an imprecise measure of time; it usually refers to humans but it could also refer to animals. In the context of the sentence above, I think 'millennia' is the most appropriate word to use. My remarks relate to British / International English; American English usage may differ.