While it certainly isn't necessary or required, after one incident, I've certainly learned to have it handy. Either the printout or at least the res# on my phone (I use TripIt).

Several years ago, I was going to check into a property (a Hampton Inn in Las Cruces, NM). Not sure what happened, but the gal immediately asked, "are you sure it isn't for the other?" And without me even answering, she picked up the phone to call them.
Before she could dial, I handed her my confirmation, and said, "my reservation is for the Hampton at (address), isn't this the location?"
She looked over my printout, and gave me a room key. Only the room was occupied, so I went back to the front. After I told her that, she gave me a key for one of their Hampton Suites.^

Not exactly sure what had happened. Perhaps the other person had my same name (I have a common first/last name), and they simply gave him my room. But I certainly was glad I had my reservation details with me

Ever since then, I've made a point of either printing out each of the reservations when I travel (only a page), or at least sending it to TripIt and having it handy on my phone. Of course no issues since then, but you never know...