I always print mine out and take it but they say you don't need to, and nobody's ever asked for it. The only hiccup I've had was when I got an email mid-trip saying they'd determined that I didn't have a machine readable passport, so my ESTA was now invalid.
All nonsense, my passport was fine and I'd just been to the US with it. And I was about to go there again a week later. A very panicky couple of days, before they emailed to say "as you were, we've changed our minds"