In the old ganster films, they used 'copper'. My grandfather, who walked a beat in San Francisco in the 30's and 40's, referred to himself as a 'cop'.
cop (n.) 
"policeman," 1859, abbreviation of earlier
copper (n.2), 1846, from
cop (v.).
http://www.etymonline.com/index.php?...earchmode=none
Interesting discussion
here.