harmonizations: 19th-century schemata
Like the rule of the octave, many of the most commonly used chord progressions have their origins in the 17th and 18th centuries.
Recent research has provided insight into 'schemata', or a set of frequently used progressions (also used within the partimento tradition). Each of these schemata has a specific function, such as closing a musical sentence, creating an ascending or descending movement, etc.
In his book Music in the Galant Style, Robert Gjerdingen discusses 18th-century schemata in detail. For more interesting examples and research, you can also visit www.essaysonmusic.com by Ewald Demeyere.
Some schemata were still in use in the 19th century in their original version, which Carl Czerny clearly shows in this Romanesca (The Art of Preluding, Op. 300, 1833).

The developments of the grand piano opened up new possibilities, resulting in modified versions of schemata, as can be seen in the examples below.
Scale harmonization by Friedrich Wilhelm Kalkbrenner taken from Traité d'Harmonie du Pianiste (1849).

Scale harmonization in chromatic contrary motion written in 1829 by Niccolò Paganini (1782-1840) for the young Clara Wieck (1819-1896).

A cadence exercise through all 24 keys by Franz Liszt (Technische Studien, book 1).


etc.
Liszt's version of scale harmonization through all keys (Technische Studien, book 8).


etc.
Chopin's Prelude Nr. 20 in C Minor is an interesting example of a harmonized prelude. It contains several frequently used chord progressions, such as cadences and large parts of the descending chromatic scale harmonization.

DIMINISHED CHORDS
The scale harmonization or rule of the octave remained one of the most important 'tonal roadmaps', but during the 19th century, there was a development towards a more personal approach to constructing chord progressions. The diminished chord therefore became very important due to its universal character, offering many possibilities to realize unexpected harmonic turns and modulations.
Excerpt of one of Liszt's many exercises on diminished chords (Technische Studien, book 8).

A sketch of one of Chopin's exercises on diminished chords for a piano method.

Two Preludes for Beginners by Clara Schumann (1819-1896) are interesting examples in which diminished chords are used, as well as other harmonic techniques such as chord connections in thirds, the use of secondary dominants, etc.

SKETCHING WITH LISZT
The sketches below provide insight into how Liszt developed ideas for preluding.
More interesting chord progressions can be found in the following publications:
Emanuele Imbimbo (1765-1839)
Gamme ou Echelle Musicale (ca.1810)
Carl Czerny (1791-1857)
The Art of Preluding, Op. 300 (1833)
Friedrich Wilhelm Kalkbrenner (1775-1849)
Traité d'Harmonie du Pianiste (1849)
Henry Lemoine (1786-1854)