After Greek Revival, there were a number of prominent "Romantic" styles fighting for the affections of the American architectural public. Let's go with the Ghibellines and leave the Goths and so forth for later. Let's see Italianate:
Yes, let's do, if it looks like that. That's the City Library in Newburgh, New York. It looks confectionery, like a lot of Italianate architecture does.
Italianate buildings were born of the "Picturesque" movement in the arts, a sort of reaction to the formality of the styles that had preceded them. They used rural Italian villas as a sort of paradigm for the style, and later had a variant that used Italian domestic city architecture as its basis. That is generally called "Renaissance Revival," but more or less it's all the same idiom.
It's exuberant, and lends itself to a certain extravagance of detail. Here's the Morse House, still in Portland, Maine. The tower is a popular feature in the style.
Two or three stories, low pitched roofs, wide eaves with lots of brackets and modillions, tall skinny windows, many with a curved top and variations of hoods over them. This is the first style in America that commonly featured a large piece of glass in the front door. Entryways were very elaborate, generally. Many elaborate porches were popular.
The interior of the Morse House shows how elaborate the whole thing could be, if you wanted.
For about thirty years, from about 1840 to 1870, it was probably the most common style in the United States. It is sparsely represented in the deep south, as the post-bellum zeitgeist didn't favor exuberance. Here's a lovely little example from Bellaire Ohio. The sled and the cooler on the stoop hints at a change in the seasons when the picture was taken. Lovely hooded windows in the flat brick facade.
Here's a more modest version being run into the ground in Cincinatti, Ohio. The fate of most of these more plebian versions was to have the brackets, porches, and prominent window trim removed and be covered with aluminum, and later, vinyl siding. You can just make out the tower with clerestory windows that likely brought sunlight into a center stairwell in this example.
There was a boom in the economy in the decades following the end of the Civil War, and people embraced the lighthearted approach and fancy decoration of the Italianate style. A financial panic in the 1870s brought an end to the attitude of frivolity, and when things got going again economically, popular taste had passed the style by. If you had dough, you'd build a Queen Anne house after that.
It had a very common iteration that you can see most everywhere to this very day. I give you: The Italianate Office Block: I never did get used to putting my money in banks in a strip mall. I wanted to walk into something like the Sprague Building, in Tacoma Washington, with its rusticated masonry and imposing solidity, and look for a bank.