Tokyo Ghoul's premiere was an experimental one to say the least. While the premise of an ordinary boy becoming a monster is a widely tackled concept in anime, and just media in general, Sui Ishida deconstructed that. Kaneki Ken, the protagonist of the series is kind and soft-spoken, even extremely observant and calculating.
Ken's quiet life comes to a close as a result of a bad date, when his crush turns out to be a ghoul and attempts to kill him. As a result, her organs are transplanted into his body to save his life. The anime sticks with this premise pretty well, but there were quite a few changes made during its debut. These are the biggest ones.
Kaneki's Torture
Rather than being taken by force in the anime, Kaneki is instead tricked into coming with Jason. In the manga, he and some of his companions are compiling bodies for Aogiri when Jason approaches him and proposes to take him under his wing, in exchange for the freedom of a mother and child.
As manga readers know, this turned out to be a lie, as he was instead tortured over a 10-day period. This timeline remains consistent with the anime, however it was only during that time that Kaneki's hair begins to slowly turn white. Moreover, Jason is breaks his promise to let the mother and child go when he makes Kaneki choose one to sacrifice. The outcome is the same, but there is a larger impact on Kaneki's psyche.
Aogiri in Season 2
Ishida wanted to take a different turn for season 2 and create an alternate continuity with similar events that happen in the manga. Unfortunately, this was best an idea left on paper, as Kaneki's personality took a drastic and confusing change. In the manga, Kaneki leaves Anteiku to make his own group with his companions.
In the anime, he instead betrays everyone to join Aogiri, so he can become more "powerful". In both adaptations, he aims to become stronger to protect his loved ones, but the manga keeps his character true to himself.
Mutsuki's Past
Tooru Mutsuki's past is only very briefly touched upon in the anime, but audiences are never shown that he was born female, and the decision to present as a man was a means to avoid further sexism or abuse.
The manga shows his difficult past with his family, and how his encounter with Torso caused his mental deterioration. The only clue audiences are given to Mutsuki's dilemma, is when the Quinx squad disguise themselves in dresses to investigate a ghoul.
Touka's Pregnancy
Kaneki's reaction and his decision to marry her remain the same in both versions, but the pace is much different. To make up for the limited time each episode had, two distinct instances were combined into one. When Nishiki tells Kaneki he's going to be a father, the first time he confronts Touka, she pushes him out. The second time, she confides in him about her pregnancy. And before they marry, Kaneki proudly proclaims that he's going to marry Touka, much to her embarrassment. Though one of the more significant moments that were cut short, was during Kaneki's internal monologue with his past selves.
At one point, they get into an argument but ultimately decide that Kaneki needs to get out alive. The reason? If he doesn't, Touka will have to name the child by herself, and she's bad with names. The exclusion of these scenes doesn't take away from the anime, but they would have certainly added to it. For the most part, many anime tend to stray away from the manga in some retrospect - but Tokyo Ghoul was one of the more infamous ones.