The title says it all, when thinking of Pirates of the Caribbean who jumps to mind the most? (probably Jack Sparrow, Elizabeth Swann and Will Turner, and after that Barbossa) Now Norrington is probably not on the top of your list.
But I say you haven't been doing him justice! And here is why.
He was promoted to Commodore.
He is obviously capable, he does his job and he does it well. (We obviously don't support his side of wiping out pirates, but from his point of view he is "Just doing his civic duty" (#Quote reference)
He is smart.
Under that ridiculous white wig he has a good head on his shoulders, a quick thinker and a capable leader, he also has a good heart.
He truly cares about Elizabeth.
We often glance over this (after all he is twice her age, and compared to Will he didn't stand a chance:) but think of it. He set out to rescue her when she was kidnapped by Barbossa and his crew, she promises to marry him if they set out to find Will, they are all gathered together and he finds out that Elizabeth loves Will and he has to put away his own feelings for her. And he gives them his blessing too, he obviously wants Elizabeth to be happy. After reading all that can't you help but feel the least bit sorry for him?
He is able to hold his own
I didn't even recognize Norrington in the second movie (I guess they wanted to give the actor a chance to look like a pirate and not "an ice cream cone" #behindthescenes) Norrington is down on his luck and seems to have thrown in his lot with pirates. But even under the circumstances he is able to hold his own amongst the pirating world and finds a way to get his "more respectable" life back.
His wits can (almost) match Jack's
Jack Sparrow is well known for his quick and witty sayings. It leaves most with a confused expression on their faces. But not Norrington, he will have a response waiting for Jack.
He let Jack get a head days start before going after him.
He was either being nice or he wanted to go home and sulk because Elizabeth's heart was meant for Will not him. (Seems like something that could be expected)
He dies because he helped Jack's crew escape.
Nothing more can be said
That concludes my list, What think ye of Norrington now?