The Two Towers
Gorbag is one of the Mordor orcs (along with Shagrat) whom Sam overhears as he is wearing the Ring and hiding in Cirith Ungol. He is also one of the orcs who finds Frodo lying unconscious in the road to the pass. Gorbag seems usually to be stationed in Minas Morgul, but he's just been ordered to Cirith Ungol. Because Gorbag is new to this duty, Shagrat has to explain to him about Shelob and even her "Sneak," Gollum. In other words, the introduction of Gorbag to Shagrat gives Tolkien a plot-level reason to explain some things about the workings of Cirith Ungol to the reader through dialogue, rather than just coming out with too many clumsy explanations as the narrator.
Grishnákh is one of the orcs in service to Sauron who cooperate (sort of) with Uglúk's men to capture Merry and Pippin and kill Boromir. Grishnákh tells Uglúk that Saruman is a traitor, and that the Great Eye (a.k.a. Sauron) is keeping said eye on Saruman. Grishnákh wants to take Merry and Pippin to Sauron's stronghold, rather than to Isengard. Grishnákh is a squat orc compared to his nemesis, Uglúk, with arms that hang down almost to the ground. When the Northern orcs all run off in fear at the Riders of Rohan, Grishnákh comes back with around forty others like him: "long armed crook-legged Orcs. They had a red eye painted on their shields" (3.3.72).
Grishnákh tells Uglúk that there is a Nazgûl waiting for them northward on the east bank of the River Anduin. Uglúk scoffs at this news, but Grishnákh clearly knows more about the Nazgûl than you might expect from an orc captain. He mentions that the Nazgûl are now winged, which may cast some light on the thing Legolas shot out of the sky in The Fellowship of the Ring Book 2, Chapter 9.
In fact, Grishnákh knows a great deal about a lot of things he probably shouldn't. When Uglúk is distracted from Merry and Pippin by the attack of the Riders of Rohan, Grishnákh seizes the opportunity to speak to the hobbits. Pippin gathers that Grishnákh knows about the Ring and tries to tempt him: "Do you want it, or not? And what would you give for it?" (3.3.111).
Grishnákh hesitates, and Pippin offers to give it to him if Grishnákh unties Merry and Pippin. Merry adds: "If we come to Isengard, it won't be the great Grishnákh that benefits: Saruman will take all that he can find" (3.3.114).
Provoked, Grishnákh drags them off into the Forest of Fangorn to search them. He is killed by a Rider of Rohan, leaving Merry and Pippin free to go off an adventure of their own. Besides providing an interesting glimpse of orc culture, with his struggles with Uglúk, Grishnákh moves the plot forward by providing Merry and Pippin the opportunity to leave the orc part of their quest and start off the Ent part. Without Grishnákh's greed, they might never have left the orc company behind.
Lugdush is one of three Isengard orcs who Uglúk sets to guard Merry and Pippin as they battle the Riders of Rohan. He orders Lugdush absolutely not to kill the hobbits unless the Riders of Rohan break through the orcs' resistance.
Mauhúr is another Isengard orc who, according to Uglúk, is planning an ambush on the Riders of the Rohan from within the Forest of Fangorn, where he waits with a small force. The Riders are alerted to these reinforcements when they find and kill Grishnákh, Merry and Pippin's nemesis; they kill "Mauhúr and his 'lads'" (3.3.131).
Shagrat is the other Mordor orc, along with Gorbag, whose conversation Sam listens to as he is hiding with the Ring in Cirith Ungol. Shagrat is a Cirith Ungol orc, unlike Gorbag, who serves with the Nazgûl. Both Gorbag and Shagrat think they have the worst duties: Gorbag is terrified of the Nazgûl, and Shagrat hates Shelob. Clearly, serving Sauron is a path fraught with perils. Shagrat's orders say that prisoners are to be stripped of their possessions but kept alive and unharmed. So Shagrat picks up Frodo and carries him off to the orc-tower. He decides that the only safe place for Frodo is the top of the tower because he wants Frodo far away from orcs who might be tempted to damage him before Frodo can be delivered to Barad-dûr.
Snaga is Uglúk's lookout, an orc from Isengard who spies only one scout of the Riddermark. He reports to Uglúk that there is only one Rider from Rohan nearby. Uglúk scolds him for not killing the man when he had the chance. Now, that scout will tell the Riders where the Isengard orcs are. This news spooks the Northern orcs from Moria so badly that they leave the Isengard orcs behind entirely and run north. Uglúk warns Snaga, "You and the other scouts ought to have your ears cut off. But we are the fighters. We'll feast on horseflesh yet, or something better" (3.3.71).
Uglúk is the captain of the orcs from Isengard who capture Merry and Pippin at the end of The Fellowship of the Ring. He wants to bring the hobbits straight to Isengard to hand over to Saruman, as he was ordered. Uglúk calls his company "the fighting Uruk-hai [...] the servants of Saruman the Wise, the White Hand" (3.3.24). Most disturbingly, he tells the other orcs that Saruman gives them human flesh to eat. Whoa, Saruman has really gone to the Dark Side.
Uglúk is the one who keeps pushing Merry and Pippin to run along with the orc company. He also has his hands full with the untrained orcs from the Mines of Moria, who don't want to run during daylight. And of course, he also squabbles with Grishnákh, an orc in Sauron's service who wants to bring the hobbits straight to Barad-dûr. Uglúk is killed by Éomer himself as the Riders of Rohan destroy his entire force.
Ufthak is an unfortunate orc who Shelob bites with her knockout (rather than instant death) poison and then leaves to hang in her web for days until his friends find him "in a corner; hanging up [...] but he was wide awake and glaring" (4.10.108). Shagrat speculates that Shelob forgot about him (luckily for Ufthak). It's this experience that teaches Shagrat that Shelob does not always bite to kill, so that she can stun her victims and eat them alive.