I'm resurrecting this as I've been wondering about the longer-term effects.
Beans, amaranth, breadnuts and other crops are all fine and good, but they are unlikely to take the place of maize. Without maize, I would suggest a severe retardation of Mesoamerican development. The cultures of the region by 1492 would probably still be in the equivalent of the OTL Archaic Age, with some horticulture, loom weaving and pottery. No large empires, no large urban centres, no largescale construction or trade networks. By extension, it is unlikely that there will be anything in the American Southwest at all. Sorry, Pueblos.
North American cultures are interesting, as prior to the arrival of maize a variety of local crops were cultivated: squash, goosefoot, mayflower and others. These were largely displanted by the coming of maize, but without that invasion it is likely that the North American agricultural package would continue to be maintained. This package was in broad terms less productive than maize, but was more sustainable in the environment and better in a nutritional sense. This would mean the expansion of Mound-building civilization would be short-tailed, but also the rapid decline of that culture (which over-reliance on maize can partially be blamed) may also be avoided. So, in the Eastern Woodlands and Mississippi we could see a culture that is less impressive than the Moundbuilders of OTL, but more enduring.
Except for butterflies, South America would probably remain the least affected. They wouldn't get corn, but potatoes and other South American crops would allow for the development of civilization here. They might be relatively behind the Inca of OTL, but only by a little.
What I'm wondering about is what would happen when the Spanish enter this situation. There would be no empires like the Aztec or Tarascan empires to simply conquer. Like the OTL Maya highlands (which took about 170 years to conquer), there would be no political centre. The populations would be comparatively much lower. There would be less infrastructure such as trade routes and roads to exploit. Much of the riches of the Mesoamerican cultures of OTL would remain in the ground.
There would be much less of an initial impetus to invade and conquer these lands, as the immediate wealth and glory would simply not be there. Gallivanting around the Mexican highlands fighting tribes that flee and attack by night, finding very little of worth, wouldn't seem very profitable. So there could be a retardant effect on the Spanish expansion into the Americas. This could also delay the discovery of the Inca (though that discovery would likely cause renewed appetite for conquest).
The effects of European diseases would probably be more devastating to Mesoamerica from a demographic point of view. When the regions are colonised, they are far more likely to require imported labour. Long term, this would mean a far more Afro-European population in the region.
What about the delay in gold and silver imports back to Spain? Mexican gold would be discovered later, but perhaps much later. Peruvian gold and silver may be exploited first, due to accessability and labour. This might have a positive effect on the Spanish economy, preventing or delaying the huge inflation of OTL.
Thoughts?