Tokyo Metro has offered the NFC capable Pasmo card since 2007 (JR East has offered the similar Suica card since 2001). You can get a Pasmo as a tourist by putting down a 500 yen deposit. At the end of your trip, you can return the card for a refund of the 500 yen, minus a 220 yen handling charge. That's an out-of-pocket expense of $2.50 at current exchange rates.
Tokyo Metro ticket vending machines also issue paper tickets. My Pasmo card ran out of funds the two days before my departure, so rather than topping it off with funds that I wouldn't have the time to use, I returned the card and bought a paper day ticket for my penultimate day.
Here in the SF Bay Area, Caltrain and BART still sell paper tickets even though both agencies are encouraging commuters to get the NFC Clipper Card. Caltrain's paper ticket fares are more expensive than the Clipper Card fares, so there's incentive to acquire the NFC card if you're a regular transit rider.
Pasmo's great. It works with the transit systems in most of Japan's largest cities, not just the Tokyo Metro. It also functions as a payment card for a lot of convenience stores, vending machines, and is accepted by some taxis.
By contrast, Clipper Card is really only good for the SF Bay Area transit systems and maybe a couple of parking garages. You can't use it to buy stuff.