Time was, they displayed a replication of the officers' badge or arm patch. Very often, it was some version of the state flag intertwined with wreaths and heraldic emblems commemorating the town's, city's or state's history or symbols. Latin inscriptions weren't uncommon.
There was plenty of "diversity" in the colorful designs—enough so that, as with US soldiers of different services involved in joint maneuvers, there was a robust trade in insignia. The walls of many police departments, indeed, remain festooned with such memorabilia.
I live (and grew up) just outside the US capital in Montgomery County, MD. For generations, cruisers here bore large, impressive door emblems that included the coat-of-arms of founder and Revolutionary War hero Richard Montgomery.
Some still do. But the design is being phased out; much smaller emblems and jazzy stripes are replacing it. [Ask Montgomery Country why.]
For their part, Metropolitan Police cruisers in nearly Washington, DC, also used to sport a compelling emblem, dominated by the US Capitol dome. Well, that gave way to three curious red stars surmounting two red dashes.
Apparently, civilian police administrators foresee the day when officers from the Third World or their children will equal or, maybe, outnumber majority Americans. Then, maybe the escutcheon will be Jesse Jackson's Rainbow flag or similar.
And why not? Already, besides Washington's, patrol cars of many departments around the country just say "Police". (Still in English— so far)
David Walsh (send him email) is a freelance writer/photographer (Click here to view his work) in the Washington D.C. area. Among his recent articles is an exposé of Hispanic drivers' disproportionately poor safety record.