Do not trust the Webster_1913 entry below, it's is just plain wrong. Finns, or any of other peoples Webster lists, are not Mongolian. This theory was the accepted one in 1913, but it was ultimately based on Swedish ideas of racial superiority over other European peoples. This is one of the precursors of the "superior Aryan race" theory. (And, in the Devil's advocate point of view: even if the Aryan race is superior, excluding parts of it for obscure reasons is still not right.)
One piece of evidence misinterpreted are the European people of Sami, who live in north Fennoscandia and speak an Uralic language of the Fennic branch. Stereotypically, their hair is dark, and stature short, which lead to theories about genetic or linguistic relationships to Asian peoples, even if they look like nothing but Europeans. Aggravating this problem of misinterpretation are some Asian and Turkic peoples speaking Uralic languages, such as the Nenets. In reality, the Sami, if anyone, are original North Europeans, having lived in North Fennoscandia long before the Finns (or recent immigrants such as the Scandinavians). The origin of the Sami is unknown to this day: the genetic "Sami pattern" is not found anywhere else. Nevertheless, their European genetic origin has been confirmed by DNA studies.
While the Finnish genes show some relation to the Sami, Finns are of the same stock as Balts, Germans, Russians, etc. Finns are one of the oldest peoples in the whole Europe. On a genetic map, the Sami stand out from the rest, the Finns a little less, and the Estonians share about 2/3 of the genes. According to Marja-Liisa Suontaus, 25-50% of Finnish genes are Baltic, about 25% are Siberian and 25-50% are Germanic. The total amount of "Asian" influence is about 1.5%, not much different from the surroundings.
The old theory caused problems with e.g. the Oriental Exclusion Act. Mr. Charles Kangas speaks at the time when Oriental Exclusion was in force:
The chief physical characteristics of the Mongolians are as follows: They are short of stature, with little hair on the body or face; they have yellow-brown skins, black eyes, black hair, short flat noses, and oblique eyes. ... They (Finns) are almost universally of light skin, blue or gray eyes, and light hair. No people of foreign birth applying in this section of the country (USA) for the full rights of citizenship are lighter skinned than those born in Finland. ... Confessedly Finland has often been over-run by the Teutons, and by other branches of the human family who, with their descendants, have remained within her borders and are now called Finns. They are in the main indistinguishable in their physical characteristics from those of purer Finnish blood. Intermarriages have been frequent over a very long period of time. If the Finns were originally Mongols, modifying influences have continued until they are now among the whitest people in Europe.
This letter was from a judge who ruled that Finns
are not subject to the Oriental Exclusion Act
Currently, it's been debated what you have to be to be a Finn. For example, the "Finland-Swedes" are Finns speaking Swedish for one reason or the other. Another one is immigrants. Anyone can be an American, if an hyphenated American, but Finns find it difficult to name first-generation immigrants Finns irrespective of legal nationality. Second-generation immigrants, provided that they can speak Finnish without any accent (or with a local accent), are usually considered Finns, especially if they have a Finnish parent.
By the way, Finns don't call themselves "Finns" or "Finnish" - it'd be hard when the sounds F or SH doesn't exist in native Finnish at all! One theory is that "Finn" is the same root as "find" and "wanderer". Another theory is that the "fen" (suo) is a translation of the originally Baltic loan zeme, which means "earth, ground, bog".
In modern Finnish, it's suomi (root: suome-). So, the country is Suomi, the language suomi (or Finnish language suomen kieli); a Finn (noun) or Finnish (adjective) is suomalainen. (The root is suomalais-; e.g. suomalaissyntyinen "Finnish-born".) I think the word "Finn" is unaesthetic, but it's better than mispronouncing and misconjugating suomi beyond recognition. Already the Estonians call us "soome".
Finnish Genealogy Society, Mailing list. A message from SOCOHONTIS@aol.com. URL: http://www.genealogia.fi/plark/finngen/1999_09/msg00058.html
Suomalaiset Pakanasivut: Suomalaisten alkuperä.