To get a good answer to this you'll need to be much more specific. Styles of hats for men and women were changing constantly and new styles came out at least every month. Fashion plates from the era, like those from Ackermann's Repository or Costume Parisien, often even have plates devoted to just a small variety of hat styles. Men's hats sometimes vaguely resemble what we consider a top hat today, but the size and shape varies as does the name (Chapeau Americain, Praugue, Cintré, etc.). Other styles like bi-cornes can be found as well. Women had bonnets, hats, toques, and turbans in overwhelming variety. Given a month, year, level of formality, and even a color choice you could likely find at least 5 options that we still have images of today.