I always print my airline, rental car and hotel confirmations.
You just never know when you'll need them.
* When I flew to Mexico on one airline and returned on a different airline, first airline would not allow me to check-in without proof of the return.
* I've had hotels try to charge me a higher rate and I had printed proof of the lower rate I booked.
* I save all my old boarding passes as souvenirs. Boarding passes on phones disappear after so many days.
* Just this week trying to get missing Skymiles from Hertz and Delta asking for copies of the rental contracts which I also save.