Anyone who tries to trace their family tree hopes, sooner or later, to find medieval nobles in it. As a medievalist, I get periodic requests from genealogists hoping to figure out if great-grandpappy really was Duke of Something. The answer is, "Maybe."
First, if you really were in the official line of descent from William the Conqueror, you'd already know about it. Noble families have kept very close track of their inheritance since the eighth or ninth centuries. France officially abolished hereditary aristocracy at the time of the Revolution, but 225 years later there are still plenty of families who know, accurately, that they would be viscounts (or whatever) if it weren't for that pesky detail. England still has hereditary aristocracy, all spelled out in the Peerage. So let's face it. We're all peasants.
But that doesn't mean that there might not be an aristocrat back there somewhere. Plenty of children got born "on the wrong side of the blanket," as some euphemistically put it (see my post on medieval bastards). And if a duke's daughter married a count (women were more likely to marry down the social scale than men), the count's daughter married a castellan, and the castellan's daughter married a knight, whose daughter married a rich merchant, and so on, then noble "blood" would be in their ancestry, even if it was forgotten after a few generations.
Given that there are far more people of European ancestry alive now than lived in the European Middle Ages, we're all related to each other and all have some common ancestors. This is true of most Hispanics and African-Americans as well as us whities. Alex Haley, who famously wrote Roots in the 1970s about his African ancestors, also had Irish ancestors. (The story, not sure if it's true, is that Irish archivists were happy to have him searching for his Irish ancestors until they found out he was Protestant.)
So how to find Great-grandpappy the Duke? It's not going to be easy. For starters, most Americans have no ideas of the names of their great-grandparents, and that's only going back a century or so. If your family has been in the US for a while, you can probably figure it out using sites like Ancestry.com, which have digitized and made searchable a stunning number of census records, birth certificates, marriage records, street directories, and the like. I've gotten my own Brittain ancestors figured out back to a Britton who came to New Amsterdam (now New York) from England in the seventeenth century.
But the jump from Europe to the US can be problematic. For one thing, just knowing one's ancestors were from "Germany," for example, isn't going to make it easy to pin them down, especially if they had fairly common names. And even if you can get your (peasant) ancestors in Europe traced back into the sixteenth century, it's going to be virtually impossible to get further.
This is because parish registers, recording births, marriages, and deaths, only started being kept in the sixteenth century. Earlier, no one bothered writing these things down. And of course parish registers, being local and kept in only one copy, have been lost in huge numbers.
Sometimes people end up tracing just their last name, in the hope that this will identify their ancestors. But last names, which only started being used for the first time in the late Middle Ages, were usually either nicknames, which could vary within the same family, or loconyms, place names, where everyone, lord and peasant, who came from the same place had the same last name.
Enterprising businesses in the US will sell you "your family coat of arms." Because there is nothing official about coats of arms in the US, it's easy to do so. Either they sell you a coat of arms of some aristocratic family with a similar last name, or they'll just make something up. My dear father-in-law had a "family coat of arms" that he'd bought, mounted over the fireplace. I never told him that his ancestors were not aristocrats. His last name came from French peasants (probably from Normandy) who came to French North America in the seventeenth century.