South Korea has announced a plan to remove all coins from circulation by 2020. Paper currency will remain, at least for now. They may be first, but I can't imagine they'll be the last. South Korea to kill the coin in path towards ‘cashless society’
Admittedly, their coins are pretty worthless - as noted in the article many of them cost more to make than they are worth. The US is in the same boat with the cent and nickel, inflation has rendered them useless.
In an interview from the 1990s, one of South Korea's main currency designers from the 1960s and 1970s said that coin production was wasteful and funds would be better spent elsewhere. Getting rid of coins, or doing an overall restructuring of the currency system in a reform (dropping "two zeroes") is something that South Korea has been contemplating for some time. I wish that would happen instead of getting rid of the coins altogether... As a foreign visitor, and non-"T-Money" card user, I find that the most useful coins are the 500 Won and the 100 Won coins, since the lower-cost items are almost always priced to the nearest 100 Won (9 cents in USD), and have been for a while. The two smaller coins still in circulation, 50 and 10, are irritatingly given as change only in certain transactions, like fees to enter a tourist attraction, or for bus fares. I cannot imagine Koreans getting rid of cash (notes) altogether. There'd be no "secure and secret" way to, uh, "grease the wheels" as it were. Speaking of which, the Bank of Korea counts used banknotes and coins that come back into the Bank's control, and calls the percentage that return as the "collection rate": The “collection rate” for smaller denomination banknotes (1,000; 5,000 and 10,000 Won) is not bad, at over 90%, while the Bank is reclaiming less than 60% of the newer-introduced (2006) 50,000 Won notes. The reason for this is that the 50K notes are popular in the "black economy" of gambling and organized crime activity. As for coins, the Bank of Korea considers the little copper-coated aluminum 10 Won coin as a particular irritant with its low collection rate of 3.7% (in 2014). This means that when 100 of the coins are issued into the market, less than four are recovered by the Bank of Korea.
Maybe not for circulation but just for "sales purposes," i.e., collector sets and gift sets? Sweden still has banknotes, from what I understand, but as money, notes comprise a tiny percentage of transactions there. South Korea still mints One Won and Five Won coins for mint sets, but they haven't been seen in circulation since the late 1980s. I guess they found out that they can make money by minting them as a part of mint sets to collectors. Each set contains 666 Won of coins, but they sell at the Bank of Korea Museum building for 8,000 Won. Not a big "Ka-ching," but a "ka-ching" nonetheless.
Yep collectors are suckers and mints around the world discovered that long ago. A lot of small realtively poor countries created many varieties of Non Circulating Legal Tender just for the purpose of sell ing them to collectors to make money. We would make fun of places like the Marshall Islands and Isle of Man for all their NCLT issues. (Liberia the country that celebrates everyone else's history and pop culture.) But in the latest 21st century Standard Catalog, do you know what country fills up the MOST pages now with their NCLT stuff? CANADA!! at roughly 105 pages. Somewhere between 5 and 7% of the entire book. (Think about it. This century is only 15 years old and they've got 105 pages already! There is so much NCLT stuff out there that the 21st century book is already approaching the size of the entire 20th century book.)
Cashless countries will likely proliferate in the not too distant future. Investopedia lists these countries that are either highly considering the move or already well on their way: Australia, Belgium, Ecuador, India, Kenya, Singapore, South Korea and Sweden. Plus, Amazon opened a prototype grocery store that requires no cashiers. Customers go into the store, scan items with their phones, and leave. No human interaction necessary. And no need for physical cash. If this scheme catches on then the end of circulating cash can't be too far behind. Digital bits will have prevailed.
I can't speak for the others on the list but Australia isn't even remotely close to becoming a cashless country.