Look at a Susan Anthony or Sacagawea dollar. In the mid-1800s a penny was the same size and made of about the same amount of copper. A dollar was roughly an ounce of silver and twenty dollars was a little less than an ounce of gold (from the centuries-old standard that gold should be worth about 17 times an equivalent weight of silver).
Our dollar today is worth about what a penny was worth when my great grandparents were kids, both in purchasing power and in intrinsic value. Back in the 1850s Congress ditched the half cent, presumably because they found it to be a useless denomination.
In the mid-1800s, a dollar could buy a night's stay in a luxury hotel or dinner for two in the dining room. Now it costs a hundred dollars for either. Since today's "dollar" has so little practical value, hardly worth an original penny, it seems the smallest useful denomination now ought to be the half dollar, equivalent to the half cent of 1850.
In 1982 the mint changed the composition of the penny from copper to copper-plated zinc, a cheaper metal, so that the melt value of pennies henceforth wouldn't exceed their face value. Congress fears your reaction, though, if it were to abolish the Lincoln cent, not to mention the useless nickels and dimes that have so little comparative value today. If you are a merchant, would it matter to you that you could no longer charge 99 cents but might have to admit that the real price is a (Sacagawea) dollar?
Congress also fears your reaction if it were to abolish the dollar bill, which is a damned nuisance and expensive to produce relative to its face value and life span of 18-22 months. Imagine that both paper cents and copper cents had circulated in the 1850s. (Paper "fractional" currency did circulate during the Civil War in denominations as low as five cents, but was quickly abandoned after the war. Our five-dollar bill is worth about as much as the five-cent paper fractional currency of 1862.)
The half dollar could be redesigned to half the weight of the Sacagawea dollar, the quarter to half of that, if we still need quarters. If we were to add a five dollar coin, then our change would consist of three or four useful denominations, and paper would start at the $10 level.
This is just one sensible idea that you will never see implemented. The dominion to our north may have the courage to do it within our life span, though. What say you, O Canada?