Coins cost a lot of money to make. A quarter (the most efficient) costs about 7.5 cents to make while a penny costs 70% more than its face value ($.017) to create. They're unwieldy, almost no one likes them and most people just throw them in a jar or can when they get home for a yearly trip to a CoinStar machine. Coins are not worth the effort it takes to make them, is what I'm saying.
On the other end of the spectrum, $50 and $100 bills are the vehicle of choice for high-end crime (a cash only business) including human trafficking, drug cartels and arms deals. Oh, and North Korea has managed to produce perfect copies of US $50 and $100 bills, so our continued use of them enriches the Kim dynasty.
That pretty much leaves the $1, $5, $10 and $20 bills as being the most common while also being in denominations too small (save, perhaps, the $20) to be used effectively for high crime.
With the prevalence of digital technology, and the far superior nature of cryptography (Both in cost and effectiveness) to currency security, I see no reason we need a physical currency anymore.