There are two different types of tropes: Character tropes and Plot or Story Tropes. Below is list of both taken from a variety of sources (as well as my own reading). But if you’re looking for a few more excellent lists, please visit The Risky Regencies blog post on tropes and Mindy Klasky’s post.
Character Tropes:
The Dandy (well-dressed ne’er do well who either gets reformed or secretly cares)
Rakes (womanizer, gambler either gets reformed or secretly cares, like the Dandy)
Athlete/Member of Four-in-Hand Club
Spy
Dukes (either a snob or someone who rejects his position)
Governess
Bluestocking/intellectual
Soldier
Thief/highwayman/con artist (could be male or female)
Commoner
Demi-monde/light skirts
Spinsters
Snarky old lady
Widows/Widowers
Inventors
Artists/Musicians/Writers
Heroes who have a profession
Naval/Sea faring
Childhood Friend
Story Tropes:
Someone is beset by Scandal
Beauty & the Beast
Estranged Lovers reunited
Friends to Lovers
Enemies to Lovers
Marriage of Convenience
Compromised
Mistaken Identity
Rags to Riches
Wounded Hero/Caretaker Heroine
House Party
Masquerades
Road Trip/Runaways
Amnesia
Wagers/bets
Hidden treasure
Murder(s)
Wills (tricky provisions and/or inheritances that play a major role in the plot)
Romance with someone of another class (usually lower)
Smuggling
Politics/Parliament
Handicapped (could be hero or heroine or secondary character whose handicap is an issue)
Social Issues (including slavery, abuse of children, etc.)
Farming/Raising Horses/Animals?
Christmas (and perhaps other holidays)
India/Other foreign travel?
Children (stories where a child or children play a significant role in bringing the hero and heroine together)