I am excluding the Caribbean because that would probably mean too many options. Here are the options with pictures and my thoughts about it:
I, like anyone else, am probably biased toward what I was first taught. I like it, but I don't know if there is a decisive argument for or against it.
The one I believe is the most common in the United States. In this case, the continent would be divided between North and South America only.
I see this one when someone says that the definition of a continent is a large contiguous landmass, and the other responds "So North and South America are different continents, they're separated by the Panama Channel". I personally find this one a little bizarre, but if Istambul can separate Europe and Asia, Panama might as well separate America
Also known as "Anglo-Saxon America" here, to me this one seems to put socioeconomical factors over geographical ones, and puts Mexico in Central America. Possibly my least favorite