TL;DR: Those mentioned in my answer are:
- Davos Seaworth
- Amory Lorch
However, it's likely most lowborn people who come to a higher position later in life are likely illiterate.
As for members of the Night's Watch I couldn't find any explicit case but it wouldn't be surprising to know if they have had an illiterate member in the higher ranks.
"You do it. They have parchment and ink at the Citadel, as well as longbows. I will expect you to continue with your practice. Sam, the Night's Watch has hundreds of men who can loose an arrow, but only a handful who can read or write. I need you to become my new maester."
A Dance with Dragons, Jon II
If we consider First Rangers and Wandering Crows as higher ups/commanders in the Night's Watch then there's probably been a good few among them who were illiterate. Assuming from the known names that if someone has a surname, and so a House, they likely had a Maester's teaching then we have no known illiterate First Ranger but we have a few Wandering Crows who have no House: Conwy, Dareon, Gueren and Yoren.
Opening this up to any Lord we have the case of Lord Davos Seaworth who could not read or write.
Obediently, he selected a paper at random. "It looks handsome enough, Your Grace, but I fear I cannot read the words." Davos could decipher maps and charts as well as any, but letters and other writings were beyond his powers. But my Devan has learned his letters, and young Steffon and Stannis as well.
A Clash of Kings, Davos I
"I am lowborn," Davos reminded him. "An upjumped smuggler. Your lords will never obey me."
"Then we will make new lords."
"But... I cannot read... nor write..."
A Storm of Swords, Davos IV
Davos' case is of course different to most Lords as he was lowborn and rose to be a knight and a lord later on in life so never got a Maester's teachings early on. As this story is likely similar to other people we could probably safely assume Ser Bronn of the Blackwater is also illiterate as mentioned in @dna's answer.
Bronn grinned. "My knightly sigil. A flaming chain, green, on a smoke-grey field. By your lord father's command, I'm Ser Bronn of the Blackwater now, Imp. See you don't forget it."
A Storm of Swords, Tyrion I
Bronn later marries into House Stokeworth and becomes their Lord.
"Bronn put a dagger in his eye, and told me I had best be gone from Stokeworth before the sun went down or I'd get the same. He said he'd pass me around to the g-g-garrison, if any of them would have me. When I ordered Bronn seized, one of his knights had the insolence to say that I should do as Lord Stokeworth said. He called him Lord Stokeworth!" Lady Falyse clutched at the queen's hand. "Your Grace must give me knights. A hundred knights! And crossbowmen, to take my castle back. Stokeworth is mine! They would not even permit me to gather up my clothes! Bronn said they were his wife's clothes now, all my s-silks and velvets."
A Feast for Crows, Cersei VII
In fact it is explicitly stated by Tyrion that Bronn could not read.
That night, when the Red Keep was dark, Bronn arrived to find him sealing a letter. "Take this to Ser Jacelyn Bywater." The dwarf dribbled hot golden wax down onto the parchment.
"What does it say?" Bronn could not read, so he asked impudent questions.
A Clash of Kings, Tyrion X
In the show we also have Ser Amory Lorch who accidentally sent a letter to House Dormand instead of House Marbrand because he could not read it.
Tywin Lannister: Can you read? My lord? Can you read? This letter detailing our infantry movements was meant for Lord Damon of House Marbrand. It was sent to Lord Marlyn of House Dormand.
Armory Lorch: My apologies, my lord.
Game of Thrones, Season 2 Episode 6, "The Old Gods and the New"
As @DariM points out later in the same episode Tywin tells Arya of Jaime struggling to read and so Tywin taught him himself. It also appears from the below that Jaime is dyslexic.
Tywin Lannister: Who taught you to read?
Arya Stark: My father, my lord.
Tywin Lannister: Hmm. I taught my son Jaime to read. The maester came to me one day, told me he wasn't learning. He couldn't make sense of the letters. He reversed them in his head. The maester said he'd heard tell of this affliction and that we simply must accept it. Ha! After that, I sat Jaime down for four hours every day until he learned. He hated me for it, for a time. For a long time. But he learned.
From this we can infer that low or high born in Westeros not everyone will be able to read even if they have access to a maester's teachings. Jaime can only read now because Tywin did not give up when the maesters had already done so.
In the Dunk and Egg stories we also learn that Dunk, later Lord Commander of the Kingsguard, is illiterate.
The old man had ridden with some of these knights; others Dunk knew from tales told in common rooms and round campfires. Though he had never learned the magic of reading or writing, the old man had been relentless when it came to teaching him heraldry, often drilling him as they rode.
The Hedge Knight
Dunk the lunk, thick as a castle wall. He felt his cheeks reddening again. Gingerly he took the parchment from the maester and scowled at the writing. Not a word of it was intelligible to him, but he knew the wax seal beneath the ornate signature; the three-headed dragon of House Targaryen. The king's seal. He was looking at a royal decree of some sort. Dunk moved his head from side to side so they would think that he was reading. "There's a word here I can't make out," he muttered, after a moment. "Egg, come have a look, you have sharper eyes than me."
The Sworn Sword