In the ongoing uproar over the latest immigration reform bill, I'd like to say that I am ASIGH and proud. That's Anglo-Scot-Irish-Germano-Huguenot. There's some Swiss on my father's side, maybe a bit of Welsh, too, but that made the acronym unwieldy. (This conservative is very much in favor of immigration and immigrants, so long as everyone abides by the rules. The best jobs I had in high school were working for men with names like Athanasios, Hieronymous, and Georgios.)
Of course, eventually you have a statute of limitations on your immigrant status; at its nearest approach, I'd have to say I'm just a fifth-generation American (via Scot-Irishman James Mack, who came from Belfast to Charleston in 1825). The English (Parris, Ensley, Pinckney, Routledge), Scot (MacLeod, MacDowell), Irish (Brookshire, Kelly), German (Schluter, Weiss, Pullig, Marstellar) and Huguenot (DuTartre, D'Oyley) all date from earlier than that; so does the Swiss (Rebsamen).
In fact, though my Parris and DuTartre ancestors both arrived in the 1600's (to Massachusetts and South Carolina, respectively), my wife wins on the "First American" question -- her great-great grandmother was Cherokee.