There are so many and from so long ago! One that sticks out from my youth is Inspector Luger from Barney Miller. Even earlier was Murray the Cop on The Odd Couple. There was Howard, the paramilitary paranoid on Hill Street Blues. Was Sippowitz too major a character to be annoying on NYPD Blue? Not to me, I found him really annoying.
Ok, nominees please.
Leaps on hood of speeding car
Ah, Shatner is classy in everything he does!
The SVU squad.
Can you pick one?
All of them.
The entire squad seems to try to one up each other with issues and self righteousness. I finally bailed on it for good by Season 4, but wasn’t bothering to catch eps from about mid S2 on.
Saw the thread title and thought of Murray the Cop but I see that covered by the Op.
Along with Inspector Luger there was also Officer Carl Levitt.
Does Lieutenant Horatio Caine of CSI Miami count as a cop? If so he was the worse ever and by far.
Joe Friday was so annoying it became a running joke.
“Just the facts, Ma’am.”
Sure he counts. Perhaps I was dazzled by his bold sunglass removal scenes, or I might have thought of him sooner.
I haven’t seen Hill Street Blues in a loooong time, but I don’t remember thinking of Howard as annoying so much as a monomaniac. IIRC, he was really competent and professional in those few situations where his skills were needed, but otherwise he had no idea how to act. He had a hammer, by god, and every problem was a nail!
I watched one episode of SVU, and decided I didn’t need to spend another hour having Mariska Hargitay sneer at me, so that was that.
I know Barney Fife was supposed to be annoying in a funny way, but I always thought he was just plain annoying.
Pretty much everyone on The Wire was annoying in their own way.
I don’t think it is fair to include Inspector Luger in this. No doubt he was an annoying TV cop, but his was a recurring guest role specifically written to be annoying, or at the very least to be Barney’s antagonist whenever he showed up. He was written as over-the-hill, out of touch and self-absorbed, so you really can’t fault him for coming off as annoying.
Levitt, on the other hand, was one of regular cast and, undoubtedly, annoying in his earnestness. I wouldn’t count him as among the most annoying, though.
My vote, however, is Vincent D’Onofrio as Detective Goren on Law and Order: Criminal Intent. That smug, know-it-all really got under my skin.
Just how was he smug? He was quite aware of his failings.
Horatio Caine and Callie “Oh, wait!” Duquesne. Worst. Ever.
Most annoying cop on a cop show, or most annoying character who was also a cop, although not on a cop show?
If the second category is in play, I have to nominate Brad Garrett’s Robert Barone on “Everybody Loves Raymond”.
Callies hotness excuses it all 
Not once did Webb’s Sgt. Friday say those words. Like “Play it again, Sam,” he’s most famous for a misattributed line.
A couple choices:
Capt Donny Cragen on L&O mothership (can’t speak for SVU). I never realized until watching his seasons again what a pain in the ass he is. He’s everything you expect from NYPD: surly, combative, never has a nice thing to say. He provided snark more than leadership. No matter what action you took, he could find something snarky to say about it. Maybe he’s the poster boy that quitting drinking does not always make you a better person.
Joe Fontana, L&O mothership again. Smug, bully, jerk-ass; most likely corrupt (they left enough hints that he was, but never followed through). I mostly skip any of his episodes if I stumble across one.
Lt (no first name) Columbo. I always wondered what his fellow cops thought of him. He was a Lieutenant, but never seemed to have anyone working under him. He never had a partner. As for his detective skills, my dad likened him to the KGB - find someone available and make them guilty. (yes, he always got the right guy, but he had help - the writers. In real life, I’m not convinced his style of detecting would net such a high success rate). To be fair - there are many good episodes.
Brenda Leigh Johnson. Man I hate her. The whole world lives to serve her. Hers is the only life that matters. She’ll use anyone - her staff, Pope, Fritz - in any way necessary and doesn’t even notice. She’s notorious for the double standard. She’s the spoiled cheerleader who everyone covers for, and no one ever called her on her BS. Plus, she has no trouble breaking the law if it suits her, including arranging murders of suspects if she can’t get a conviction. (plus I blame her for NOT killing Stroh when she had the chance, making us long-time fans endure the conversion of Major Crimes into The Rusty Show). And worse, she makes me watch her show, AND own all the DVDs! She has Powers, man! 
I think I’d call Brenda evil rather than annoying. But Fritz! He’s such a pussy and got run over by Brenda pretty much every day – that was really annoying.
You know, you’re probably right.
I’m an “old school” cop show watcher. The leads are supposed to be likeable, and NOT the bad guys. Even cops like Hunter were still the good guys. They may be Lone Wolf Rogue Cops who Can’t Follow The Rules, but they were at heart honest. They only killed bad guys. They cared about evil and social injustice. I still expect that the heroes of the show are generally good guys.
I could never watch The Shield because the main character starts out as a murderer. But Brenda snuck up on me. The writers skillfully made me take her side, especially how the old line cops - Taylor, Flynn, that other RHD asshole - all were against her for no good reason. Then they sprung it on us that she really was evil, after it was too late and I already liked the show.