This armor still weighed down a soldier, but it was effective for resisting criminals or guerrilla fighters who could only afford hand guns. Explosives and precise or high caliber sniper fire can still bypass the armor however and only the most expensive armies could mass produce it. Still the armor have saved many soldiers lives; especially Americans active during the War on Terror.
The most infamous example of the effectiveness of modern body armor was during the February 28, 1997 North Hollywood Shootout; where police handguns were unable to harm the heavily armored bankrobbers, who wore Aramid armor from shoulder to ankle. Larry Phillips and Emil Mătăsăreanu survived the Shootout for 44 minutes before SWAT arrived with high caliber assault rifles. In response; the Department of Defense gave 600 surplus M16s to the LAPD so that common officers could properly arm themselves from such future incidents instead of waiting for SWAT.
Kevlar is the standard armor for counter-terrorist forces like SWAT and bomb squads; who are able to mobilize against a relatively slow target like hostage takers, bank robbers or bombs.
Special forces, even American ones, ignore body armor as they prefer mobility.