I went to a few interviews, and here's what I noticed: half the time people didn't take the printed resume at all, and in half of the remaining cases they asked for it kind of casually later on. But there was one time when the interviewer forgot to check my profile beforehand, and I quickly pulled out a copy - everything went smoother and faster. So I still take two or three copies with me, because it's insurance for practically nothing.
A more practical tip that'll actually help more: keep your resume in a separate folder or envelope, not just thrown in your backpack. If you pull out a wrinkled sheet from your bag - it gives the impression you weren't taking it seriously. The condition of the paper works in your favor too. And one more thing - prepare a version with slight tweaks depending on the position: maybe in one version you emphasize certain skills, in another your experience. It won't take long, but it shows you were thinking about this specific role.
Overall it's not a big deal, of course, but the habit of having a couple of copies on you - it's like bringing an umbrella before you head out. Most of the time you won't need it, but when there's a sudden downpour, you're glad you have it.