When I was growing up it was generally accepted amongst the populace that Chris C. discovered America. We now know without a doubt that the Norse got there first around 1,000 AD. I have also heard ponderings that some Irish monks may have made the journey and that there may have been some contact with Pacific Islanders. This got me wondering if there was any evidence at all of any Native Americans making it to Europe before Columbus.
There's always room for discussion, but perhaps the section Travel and contact across the Atlantic before Columbus in our FAQ will answer your inquiry.
There's some genetic evidence that Native American women (if not men too) reached Iceland, possibly hitching a ride along with the Norse, whether they wanted to or not. This is indicated by the presence of Haplogroup C1 in the Icelandic population. A haplogroup is a genetic marker that can be used to identify particularly lineages (either male or female; female in this case). Haplogroup C1 can be further divided into sub-lineages. C1a is found in indigenous peoples of easternmost Siberia. C1b, C1c, and C1d are found throughout the Americas. Iceland has C1e, which might be descended from C1b-d, because it seems to be relatively recent (only hundreds of years old rather than thousands), but there's a slight chance that it was brought westward into Scandinavia from Siberia, too.