The Bank of Korea is planning for a cashless society by 2020. Swedes are making the shift. I am intrigued but also troubled.
There's a lot to like about the idea of a cashless society, starting with its effect on crime. The payoff to mugging people or snatching their bags has already declined dramatically, simply because fewer and fewer people are carrying cash around. I myself almost never have any of the stuff on hand. If it weren't for the rising value of mobile phones, street crime would have largely lost its profit motive ... and if better phone security makes it impossible to repurpose a stolen phone, that motive will approach zero.
A cashless society would also see a decline in the next level of robberies: stickups of retail outlets. There's obviously no point in sticking a gun in the face of some liquor store clerk when all he can give you is the day's credit card receipts. Even if these sorts of crimes are replaced by electronic thefts of equivalent value, this would still be a major improvement for society, simply because the threat of violent crime is uniquely terrifying and corrosive to community.