Many thanks for the responses to my previous post from my regular readers (all three of you). Between you, you managed to name most of the major food products or ingredients that come from the Americas and were unknown elsewhere in the world until the 16th century. There's still a few more than didn't get named, but sufficient time has passed and it doesn't look like I'm going to get any more responses.
Here is the list I had in mind, after much consultation of Wikipedia. I may have missed a few myself, so feel free to point out any other products I might not have thought of.
Maize / corn
Chocolate / cocoa
Common bean (green, red, black, yellow, pinto, etc)
Squash family (including courgette, marrow, pumpkin)
Coca (as in Coca Cola, so yes it qualifies as a food ingredient or flavouring, as well as a narcotic).
Related to the last item, apparently Latin America is also home to about 85 percent of all known hallucinogenic plants. As far as I know no one has a really good theory about why that is.
The American origin of many of the above comes as quite a surprise (or at least it does to me), given how inherently globalised they seem. It's therefore interesting to reflect that none of the following are native to Latin America and were unknown there until the 16th century: