Reply #27: The correct term, according to the INS, is unauthorized aliens

[Xipe Totec]

or Unauthorized migrants

Unauthorized aliens include those who enter the United
States without documentation or with forged documentation;
lawfully admitted immigrants who remain in the
United States after violating immigration law; and aliens
who have entered the United States on a temporary visa
and remained past the time limit of the visa.

Immigration Policy in the United States, Page 23:

http://www.cbo.gov/ftpdocs/70xx/doc7051/02-28-Immigration.pdf