Game of Thrones contains large amounts of pragmatic adaptation largely due to the transition from a rotating third person limited POV series of novels (complete with inner monologues) to a televised ensemble piece. Some changes worked better than others.
The show excises flashbacks and prophecies entirely. Flashbacks would require the expense of hiring an entirely different cast, while prophecies are tricky to write and pay off in a satisfactory manner. Because of this, Daenerys' hallucinations focus on her own story, rather than long-dead characters or those that live on a different continent; Ned's memories of his sister's demise are replaced with other foreshadowing devices; while the mysterious masked Quaithe's role is altered from prophecy sounding board to a foil for Jorah Mormont. Arguably, this streamlines and improves the series greatly.
Tywin Lannister, Robb Stark, and Littlefinger were offpage for the vast majority of A Clash of Kings, but the writers of a television show could not afford to have these popular (and probably well paid) actors disappear for a whole season. So they were either moved into someone else's story (Tywin into Arya's), had the previously secondhand exploits shown first hand (Robb's campaign and courtship of his non-Frey wife), or apparently develop mysterious teleportation powers to cameo in mulitple stories (Littlefinger making deals with at least three factions of the War of the Five Kings).
Arya's story had an extensive road trip portion with multiple kidnappings, then a stay in Harrenhal where she interacts with a bunch of new characters and ends up facilitating a palace coup with even more new characters. To streamline her story, much of the road trip portion was cut out and instead of working for Weese and later Roose Bolton (who was moved to Robb's camp for character development), the palace coup was cut out, and she only served one master in Harrenhal—known character Tywin Lannister. These changes also changed the focus of her story from the suffering of the smallfolk during war to the cat and mouse game to hide her identity.
Jon and Dany's stories in Clash were very internally focused with almost no action until the respective last chapters. To make them more action packed, Jon gets separated from the group to spend more time interacting with his love interest and Dany has to deal with the kidnapping of her dragons and betrayal by one of her handmaidens.
Due to the POV structure of the book, we needed two shadowbaby assassins birthed by Melisandre in order to understand how they came to be and what they did: the one that kills Renly (which we see in action from Catelyn's point of view) and later the one that ultimately kills Cortnay Penrose (which we see birthed from Davos's point of view). In the show, we see the same shadowbaby being born (with Davos smuggling Melisandre somewhere close enough so that the assassin can kill Renly, which is seen from Catelyn and Brienne's point of view.
Related to the cutting of the second shadowbaby, Storm's End, Penrose, and the entire subplot surrounding Stannis wanting his bastard nephew's blood was cut. Stannis's family was also cut from Season 2. However, with the casting of his wife and daughter in season 3, it remains to be seen how much, if any of Stannis's family drama and Storm's End is repurposed for Season 3. Considering that Stannis does not do much except sulk in Book 3 until serving as the Big Damn Heroes for Jon at the Wall, moving the Storm's End and Stannis's family plot to Season 3 may be the most pragmatic way to adapt that storyline, especially since the third book is going to be spread out over two seasons.
Much of the dialogue of Davos Seaworth in the TV series does not appear in the books, since much of his character development in these is restricted to his inner thoughts; the fact that further books concerning Jon Snow's actions on The Wall are written like that as well, there will probably be changes in dialogue in further seasons of the TV series.
In the books, all POV Stark children whose direwolves are still alive (meaning Jon Snow, Arya and Bran) are shown warging into them when sleeping. In the series, only Bran's dreams are kept, because they are essential to his Story Arc, while Jon's and Arya's stories can work without them.
In the novels, it's Ser Garlan Tyrell who wears Renly Baratheon's armour at the Battle of Blackwater. Ser Loras Tyrell wanted the honour, but he was too short and too slender. On the show, Loras becomes King Renly's ghost because Gethin Anthony and Finn Jones (the actors who play Renly and Loras) are practically the same size.
In the books, Barristan Selmy joins Daenerys under the alias Arstan Whitebeard, which is enough to disguise his identity as Daenerys is the only viewpoint character for this story, and had never seen him before. On the show, of course, the actor is easily recognizable, so he reveals his true identity to her right away.
Loras is older than his sister Margaery in the novels, but it was revealed by Bryan Cogman in this interview that Margaery is Lord Mace Tyrell's eldest child on the show. The switch in birth order was no doubt due to the fact that Finn Jones is six years younger than Natalie Dormer, the actress who plays his character's sister. Also, Willas and Garlan Tyrell are Adapted Out (as were most of Davos Seaworth's sons), with their characteristics condensed into Margaery and Loras - notably, Margaery inherits Garlan's kinde personality and being the eldest child, while Loras inherits his elder brothers' calmer personalities and being Mace's heir. This is most justified with Willas, who remains The Ghost even as far in as Book 5.
The timespan of the series is expanded compared to the novels - whereas in the books the story has covered at most three years at the end of ADWD (Book 5), events are spaced out so that each Season covers a year's worth of storyline - an important aspect when the 6th Season will conclude Book Five's narrative, and the child actor's need their growing into adulthood acknowledged in-inuverse to avoid Dawson Casting. In addition to this, the producers have commented of how various narratives have their chronological order changed around in some cases, both to fit the medium's narrative and because you just can't have some character's drop off-screen completely for stretches of time - Theon Greyjoy thus had a subplot created for Season 3-4 (with what happened to him off-screen shown in more detail); Bran Stark's Book 4/5 narrative is both expanded-on and yet sped-up (Bran has very few chapters from Book's 3-5, so this is inevitable); Jaime & Brienne's story is shifted to give them more to do in Season 4 (and Brienne's Book 4/5 plot begins roughly midway through Season 4); and so on.