The conflict at the heart of Chinua Achebe’s Things Fall Apart is culture clash. There are different types of conflict in literature: sometimes it is a conflict between two parties; other times, it is a protagonist against nature. In this story, however, the conflict is the future against tradition.

Igbo cultural traditions play a major role in the novel—for example, the parades, the sacrifice of Ikemefuna, and ritual exile of Okonkwo. However, the arrival of Christian missionaries changes the culture. Achebe clarifies that it is not the religion that is the enemy, as the first leader of the missionaries is well received and attempts to interact with the culture instead of destroying it. However, after a new missionary comes, the society unravels. The Igbo people are encouraged to give up traditions and customs. This threatens their cultural identity and incites a violent response. The climactic revolt and attack on the mission house shows the tradition and modernity conflict come to a head, encapsulating the clash of the novel.

As the other answers to this question suggest, the major conflict in Things Fall Apart is between the native Igbo culture and that of white colonial culture. Indeed, the book ends with white colonists gaining greater and greater control over the native populations, and so much of Chinua Achebe's novel focuses on the conflict inherent in colonial expansion. The most dramatic expression of the conflict comes at the end, at which point Okonkwo succumbs to the despair of losing his traditional culture and kills himself.

However, there is another conflict at work here, the conflict between patriarchal aggression and the community. Fearing failure and weakness above all else, Okonkwo leads a strict life based on physical prowess and domination. Okonkwo views any kind of failure as weak and detestable, and so he becomes an image of the radically individualistic and proud patriarch. This aggressive pride conflicts with the communal focus and culture of Umuofia, and it ultimately leads to Okonkwo's exile and isolation. Thus, one of the book's main conflicts illustrates the damaging effect of patriarchal aggression and shows the ways in which unchecked, destructive male anger stands in opposition to the harmony of the community.

There are really three separate major conflicts in Things Fall Apart by Chinua Achebe, one of which is individual and two of which are cultural. 

On the individual level, the major conflict is that of the Igbo warrior Okonkwo in his quest to achieve greatness. His major struggle is against his own "chi" or divine nature, which does not have a great destiny. Thus, in many ways, Okonkwo is fighting against his own nature and fate, although this conflict is also externalized in the plot of the novel. He angers the earth-goddess Ani and the religious authorities and traditions of his village. After he returns from exile, he comes into conflict with the British.

On a cultural level, there are two major struggles in the book. The first is between the Igbo and the colonial British and the second is between traditional Igbo religion and Christianity. The characters of the novel are often caught between these opposing forces. 

The fundamental conflict explored by Achebe in Things Fall Apart is that of tradition versus change. The changes that take place among the Ibo people after the arrival of Christian missionaries (and during Okonkwo's exile) are profound. Many people not previously held in high esteem by the Igbo are converting to Christianity and gaining prestige as a result of their actions. When Okonkwo returns from his exile, he finds that the religion has destroyed much of the coherence of Ibo society. This trend is exacerbated by the imposition of a colonial society, complete with an exploitative palm oil industry. Even his son has joined the ranks of the converted. Okonkwo tries but fails to marshal support for a return to traditional life, and so he kills himself, having become an anachronism in the span of a single life. He is in many ways a casualty of this basic conflict.

There are a number of conflicts in the story, one of the main ones is the desire that Okonkwo feels to overcome or defeat the legacy of his lazy father Unoka.  Unoka was a lazy man who liked only to play music and drink palm wine, he died with a great deal of debt and no titles and no respect from the tribe.  Okonkwo was ashamed of him for as long as he could remember and fought against this throughout his entire life.  To overcome the stigma of being Unoka's son he worked incredibly hard to build his fortune, became a great warrior and wrestler, and refused to show any sign of weakness or emotion as he was terribly afraid to show anything like his father's personality.

This in turn led to another conflict which had to do with Okonkwo's temper and the ways that it got him into trouble because he couldn't control it.  He was unable to sit back and had to participate in the killing of Ikemefuna, he fired a gun at one of his wives and even beat another wife during peace week, all of which resulted in serious consequences.

Another major conflict has to do with the problems that arose when the missionaries arrived and began teaching the tenets of Christianity and they were in serious conflict with the traditions and beliefs of the tribe.  This put the believers in the new faith in direct conflict with the supporters of the traditional practices and ways of worship and led to what some consider the destruction of the Igbo way of life.

What are some conflicts in Things Fall Apart by Chinua Achebe?

Things Fall Apart by Chinua Achebe is what is sometimes known as a "postcolonial" novel, meaning that it addresses the effects of European colonialism and its aftermath on a non-western society. Set in Nigeria, Achebe's novel tells the story of how the Igbo people respond to the colonial situation.

The first main conflict within the novel is that of Okonkwo, who struggles to become a great man and warrior, despite his mediocre "chi" or spirit, in a way that defines success in a traditional Igbo manner, but also puts him in conflict with tribal custom.

Next, we have a conflict between traditional Igbo religion and the newly introduced religion of Christianity.

Another type of conflict is based on gender, with the Oracle of the Hills and Caves being an example of female power and Okonkwo of a male who suppresses his feminine side and thus is considered unbalanced by Igbo standards.

Finally, we have a conflict between the white colonial powers and the Nigerians.

In Things Fall Apart by Chinua Achebe, what's the resolution of the main conflict?

In Things Fall Apart, the main conflict is that Okonkwo can't accept the changes that Christianity and westernization have brought to his village. He has always gotten prestige and esteem from his village by being a strong wrestler and by being unfailingly willing to display traditional masculine behaviors. For example, he even kills his adopted son, Ikemefuna, whom he loves, because that is what the oracle of the village decrees. However, when he is in exile for killing a man at a funeral by mistake, the town changes, so that Okonkwo's values and traditions are no longer the accepted ways of doing things. Christianity draws the weaker members of the village, including his own son, and Okonkwo retaliates by burning down the church. In response, the white foreigners imprison the tribal elders, and it's clear that the whites have the upper hand in the conflict between traditional and new values. To resolve this conflict, Okonkwo hangs himself, in violation of his own traditions. This is, sadly, the only method he knows to extricate himself from the onslaught of western traditions in his village.