I'm a bit OCD on travel plans and even I haven't printed out an ESTA. If it is now a requirement, I haven't heard about it. But 20 minutes prep can save you some ballaches on travel.
1.
Photocopy of passport and DL. I've never needed to use it, but I know someone who lost their passport and said that having the photocopy sped up the process.
2.
E-ticket This is the first year I won't need it as I think you can now carry this on your phone and they will scan it. (I'm going to x2 check this before I go tho!!) Edit: Looks like you still need a paper e-ticket, but for Virgin you can get your boarding pass sent to your phone rather than hard copy. (Would be better if e-ticket was the same too)
3.
Hotel confirmation rates I have needed this twice. Once when a hotel refused to believe I had a booking and once when they tried to convince me my nightly rate was much higher than it was until I showed them and they backed down.
4.
Medical Insurance documents Needed the E111 a few times, but obv that is no good in Vegas. Thankfully never needed so far, but anyone needing treatment will definitely be needing proof, as well as contact info.
5.
Car hire voucher Obv useful if you hired a car on a voucher
6.
Proof of entitlement to funds Whilst having $20k on you isn't a problem, being able to provide a bank statement or withdrawal slip etc will at some point help you out.
7.
ITIN number Just in case...
It's only a few pages of A4, only takes a minute or two to produce, assuming you are taking a laptop etc will sit flat against the laptop and not be an inconvenience, but could save you several hassles at the other end.