In the US, a hallmark of colonial architecture was the Palladian window:
This is basically a larger, arched center window with flanking rectangular windows separated by pilasters or at least trim. In Europe this is most commonly known as a serliana, a name derived from Sebastiano Serlio whose architectural treatise describes its origins from ancient Roman triumphal arches.
However, like many classical architecture motifs, Palladio is credited largely because his work was so admired and frankly copied by so many English architects of the next few centuries, especially Robert Adam and Inigo Jones. Jones was particularly interested in Palladio's villas as models for the large English country estates he was working on at the time. That the British Empire soon flourished and spread across the world accounts for the ubiquitous of Palladianism from all far-flung colonies like India and the US.