According to Algebra.com, a dollar can be made with 25 coins by combining 3 dimes, 12 nickels and 10 pennies. There are at least four other ways to combine 25 coins to make a dollar, using American currency.
Other coin combinations to make a dollar include: 7 dimes, 3 nickels and 15 pennies; 1 quarter, 3 dimes, 6 nickels and 15 pennies; 2 quarters, 3 dimes and 20 pennies; 1 half dollar, 2 dimes, 2 nickels, and 20 pennies.
There are many obsolete coins, with odd values, that would allow for more combinations. Wikipedia lists some of these obsolete coins, such as: the half-cent, two-cent, three-cent and twenty-cent pieces. These coins can be found in collections; however, they are no longer considered legal tender, according to Wikipedia.