Just a word of advice: Before adding animations, interactions and/or a parallax effect to your project, ask yourself this.
If not, don’t do it. You don’t want to be Michael Bay, do you? Sure he makes money, but just like most of his films, they lack story and gets boring.
If you want a great site, use the power of effects tastefully.
While typically I wholeheartedly agree with the “less is more” mentality, the web is at a place that allows us to achieve so much more than it was initially capable of - and our visitors deserve the best, most enjoyable experiences we can deliver.
The responsibility falls on the creator to decide how and when (and to what extent) these techniques should be used. We (as designers and developers) should strive to provide a more fulfilling experience on the web without distracting from the overall message. Most examples of interactions are almost never necessary, but they provide unique moments for visitors that may not be expected - which in turn makes your website memorable. Ultimately, you want your visitors to be pleasantly surprised by interactions and animations, not annoyed.
That being said, adding transitions and motion across your entire website can definitely become overwhelming quickly; however, just like Photoshop filters, if these new techniques are used sparingly and without taking away from the experience of the user, they should be welcomed and explored as much as possible.