Besides Leif Erikson...
(I use the term old world to refer to any place that is not the Americas, I believe this is accurate) I’ve always speculated that there might have been other people from the old world that might have found their way to the Americas.
The first and least likely I think of my ideas is that there were just other European explorers that ended up in the Americas that were just less documented. They could have been other Norse explorers or less known Spanish or Portuguese sailors.
The second and more likely I think of my ideas would be interactions across the pacific. One location I though of was between Siberia and Alaska. It’s how people originally migrated to the Americas, and the Bering straight isn’t very long and could be crossed when it freezes or with rafts. The areas are culturally similar so I believe there is some truth to this concept
The other location would simply be Polynesian sailors ending up eventually reading the pacific coast. While I personally doubt this as the distances seem so far, I do believe this might actually be true.
So, are there any recorded instances of these ideas actually happening? If not, how likely is it that each still happened? What might have these interactions looked like? Thank.
There are various examples of Pre-Colombian Transoceanic Contact that have been documented with varying levels of evidence.
As you say, the most prominent and well-described example, fully attested in both written accounts and physical evidence, is the Norse Colonization of Greenland and North America, a contact that in various forms lasted from 1000 AD - 1400 AD.
Apart from this, there is recent, very strong evidence for Pre-Colombian Transoceanic Contact between Polynesians and Amerindians. What may surprise you is that the evidence for Polynesians visiting South America is rather weak though, instead the strong evidence is for Amerindians from the Pacific coast of Colombia visiting Polynesia around 1200 AD. The evidence for this is DNA admixture, found in a 2020 study, showing an early admixture event, possibly in Marquesas' Islands, that preceded the peopling of Polynesia, meaning many Polynesians today descend from the Colombian natives. Further evidence of this is, of course, the sweet potato, a South American staple crop present in much of Polynesia since 1000-1200 AD. In most of Polynesia it was even called Kumara, the same word as many Andean natives. This makes evidence of contact in this area basically indisputable today.
A third area in which there is some evidence for contact is Asians, specificlaly Japanese, shipwrecks in Alaska and the Pacific Northwest. The evidence for this contact is somewhat more circumstantial. In historic times, especially form 1700-1850, there are numerous cases of Japanese ships being led offshore and drifting to American shores. The incredible stories of Otokichi, and earlier of Daikokuya Kodayu serving as famous examples.
It has been speculated that these same drifts could have happened earlier, and there is some evidence, specifically metallic objects found at various archaeological sites. Find of a Chinese belt buckle dated to the centuries before 1 AD at Cape Espenberg is one example. Iron knives ahve also been recovered form the 15th century site Ozette in Washington State. The circumstances make this contact highly likely, altho it is difficult to say much for sure.
Finally, it can be said that contact was always maintained by Inuits across the Bering Strait, especially the north part of it. For them the strait was not a barrier, it was a bridge, and contact was relatively frequent across the straits, although this didn't really mean much connection between the two civilizations.
There are many more claims of potential contact, but they fall largely within the realm of pseudoscience.
Some sources:
Native American gene flow into Polynesia predating Easter Island settlement:
https://www.nature.com/articles/s41586-020-2487-2
Chinese belt buckle at Cape Espenberg:
https://www.nps.gov/articles/aps-16-1-18.htm
Japanese Shipwrecks in British Columbia, Myths and Facts, by Grant Keddie:
http://staff.royalbcmuseum.bc.ca/wp-content/uploads/2013/08/JapaneseShipwrecks-Grant-Keddie.pdf