I've seen two variants of parallax - parallax scrolling (which is fine) and parallax videos that play behind text. When you're trying to read text, having a moving image behind the text makes it harder to read. It looks cool, but it's a bad design. And not just for the readability issues, but also due to the loading. For example, PayPal has it on their front page now. I used to be able to go to PayPal and immediately click the login button. Now I have to wait for the loading to finish. It's annoying.
I find parallax scrolling to be ineffective. Call me old school but it takes a well understood action (scrolling) and overloads it to perform animations. Animations which often times do not add much value besides "flair". An ineffective tradeoff in my opinion.