After seeing the first episode of Tokyo Ghoul √A, I noticed a major difference in the anime. Are there any more differences between manga and anime (both seasons)?
Root A (season 2) is a completely different storyline that diverged from the manga and shows Kaneki if he had joined Aogiri instead of going off on his own. Though it does have some big spoilers, Read a bit about why they made this decision on This question. Almost the entirety of Root A is different, but some scenes (mostly fights) are recreated and are very similar overall. The storylines mostly merge at the last "arc" which occurs in the last 2-3 episodes of the series. This is the 2nd raid by CCG, Considering the first being the one against Aogiri (I will not say more as its Spoilers) and events play out differently but with overall identical results in the end. That is to say that major events that affected the results of the Raid occurred in both, though not necessarily in the same way. This was done presumably to leave the option to return to canon material in Tokyo Ghoul RE for season 3 if they chose to do it, but it could just be that it was supposedly the original story-line before Ishida changed it to what the Manga used, as noted in the first link, and he kept them through both versions.
Season 1 was very similar overall, with only moderate changes such as the chronology as better described by Thellimist in that answer, and a few other bits and pieces about how events occurred, primarily regarding Hinami and her Parents and how those events started up, and they did heavily censor Jasons Torture to Kaneki. He was down there for 10 days ( Read about it Half way down the page in the aogiri arc Summary of Jason on the wiki here
Overall, Season 1 is very similar, while season 2 only has bits and pieces that are similar.
[Pierrot] changed the chronology of some of the events in the manga. For instance, Kaneki doesn't meet Tsukiyama (Gourmet) until after the Hinami incident with Amon and Kado (senior) (the doves) killing her parents. I believe they changed the order of these events to make Kaneki's presence in these fights more comprehensible. For example, Kaneki is less involved and a little helpless in the church scene against Tsukiyama, even in the manga. This is a result of his starvation causing his weakened state, despite his amount of training "actually" being greater than when he fought Amon (based on the manga). But in the fight against Amon, both manga and probably TV, Kaneki is much more active and displays more tactical fighting. So it makes sense to put the Tsukiyama conflict part before in the television as a result of Kaneki being more passive and weaker in these instances as opposed to when he fights Amon, it highlights the benefits of his training and emphasizes his increasing strength. So to an extent this is interesting that [the studio] changed the chronology of these events it makes sense in an appreciable way. The censoring is ridiculous though, on an emotional level, your missing out on a lot of the show.