A few game titles have taken place in the 18th century with naval gameplay involved. Here are the game titles featuring what the some of the warships looked like according to them.
Assassin's Creed III (American Revolution)
La Belladonna, a French frigate disguised as a Spanish ship
Couldn't find any artwork of the Continental Navy's ships :(
Assassin's Creed IV (1715 - 21, set during Golden Age of Piracy)
Concept art of British brig, but with no ram
Concept art of Spanish man o' war
Spanish frigate on left, Schooner on far right
I couldn't find any concept art of any the games Portuguese ships (not even sure if the Portuguese had any naval presence in the Western Carribean IRL), but this video of one of the game's main missions features Portuguese brigs, frigates, and man o' wars
Assassin's Creed IV : Freedom Cry (1735, Port-au-Prince)
Assassin's Creed : Rogue (1754 - 60, French and Indian War)
Note: British ships in this game title looked exactly like the ones from IV
HMS Pembroke, James Cook's man o' war, against French fireships, man o' wars, and frigates
EDIT: here is a British jail ship from ACIII, and it was absolutely massive in the game
It could take a long time to answer all of this, so for the pirate era covered in the AC4, I'll sum it like this: Generally not accurate. Like other media portrayals of pirates, this game, on average, liked to use bigger ships in larger numbers than would have historically existed in that time. Ships are often more powerful than they would have been historically and had smaller crews than they would have had. Everything is oversimplified for the convenience of game design. Some things are made just to create the ability for players to "level up" their ship's abilities and have little to do with historical accuracy. Overall, like the rest of Hollywood, efforts at historically accurate portrayals of period material culture fall severely short of what was actually used back during the early eighteenth century.
