One of the most celebrated, and remembered cop shows from the '80s was Hill Street Blues, a show noted for quirky characters, but with an undercurrent of grittyness. I remember fondly the theme song, by a veteran writer of many police themes, Mike Post.
Daniel J. Travanti starred as the chief, Captain Frank Furillo, but perhaps the most most memorable line of the entire series came from the daily briefings conducted by Sgt. Phil Esterhaus (Played by Michael Conrad), who always ended each briefing with "Let's Be Careful Out There." That was a line often repeated during the '80s.
On the opposite extreme of '80s cops shows was highly stylized Miami Vice, a show oriented to the age of MTV, with colorful sets, slick background music, and fast-paced editing. The intro showed scenes of the Miami area, then popular due to the effect of Miami Vice, the popularity of South Beach style pastel colors (a fave in the '80s), and Gloria Estefan's Miami Sound Machine.
Miami Vice's hugely popular theme was from Jan Hammer.