What are some rare US coins?

There's no simple answer. US has struck coins since 1793 in about 2 dozen denominations so there are many rare ones to choose from.

The following are among the rarest. All of them are in collections so there's no chance any will turn up in change!

1854-O $20 gold piece (double eagle)

1933 $20 gold piece

1793 Liberty head cent with a chain reverse

1913 Liberty head nickel

1794 silver dollar

1804 silver dollar

1822 $5 gold (half eagle)

1796 and 1797 half dollars

All of those (and more) are worth well into 6 or even 7 figures. If you consider coins worth less than a quarter of a million dollars there are many dozens.
nickels