Dharma
Dharma is the central theme of the Mahabharata. Dharma, most simply put, is the destiny and responsibility of an individual. Everyone has a different dharma, and it is his or her obligation to follow it. Yudhisthira is portrayed as a righteous king who closely follows his dharma, while Duyodhana is said to live in defiance of his dharma. Hence, the conflict between the two that drives this story acts as a parable about man's conflict between living in accordance with dharma versus failing his dharma.
Action
As outlined in the Bhagavad Gita, action is crucial to fulfilling dharma. Throughout the epic, we see characters deliberating about whether or not to take action, and ultimately almost always choosing to take the action that is in accord with their dharma. There are also a number of actions taken impulsively or out of greed, such as Duryodhana's decision to steal Yudhisthira's kingdom or Dhrtarastra's destruction of an effigy he believes is Bhima. These instances show that while action is important to achieving dharma, action taken without detachment or proper consideration could result in sin and, ultimately, adharma.
Caste
Even though the Mahabharata focuses nearly exclusively on characters in higher, privileged castes—Brahmin, Ksatriya, Suta—the duties and dharma of those castes are profoundly important. The Pandava brothers often grapple with the dharma of their Ksatriya caste, which obliges them to be warriors and rulers often acting in conflict with more generalized principles of dharma. Much of the ethical discourse in the epic focuses on this conundrum. Characters who break with their caste are often shown in distress or committing sin, such as when Draupadi disguises herself as a maidservant or how Karna decides to live by the dharma of the Ksatriya caste despite being a Brahmin.
The Tragedy of War
In dharma, war is considered a last resort, only to be fought when all other methods of resolving a conflict fail. Duryodhana, living in adharma, violets this tenet by seeking conflict with the Pandavas essentially from the very beginning. But the people actually fighting in the war are often conflicted about the enterprise. Arjuna initially wants to throw down his arms when he realizes how many kin he will be slaughtering, and both Bhisma and Drona desire their deaths at the hands of the Pandavas once they feel that they can no longer fight in the war honorably. The death toll of the war is massive, with less than 10 warriors left on each side when it's all said and done. The funeral pyre and river ritual in the Ganga stand as one of the most affecting segments of the epic, as we fully come to terms with the destruction the war has caused.
Gods and Humans
The blurring of boundaries between the gods and humans in the Mahabharata is both a recurring trope and an important theme, as it helps wed the cosmic, metaphysical aspect of Hinduism to a material, if mythical, version of humanity. The gods are frequently disguising themselves as humans or inhabiting characters in the book, while the Pandavas are commonly understood to be incarnates of the gods while the 100 Kaurava brothers are manifestations of demons. The battle between gods and demons that opens the epic quickly spills over into the human realm, and the celestial struggle between good and evil is, quite poetically, one that humans are tasked with arbitrating.
Storytelling
As the Mahabharata is itself a framed story, dictated by Vyasa, storytelling is foundational to the epic unfolding. But even within it, all manner of parables are recited to clarify moral matters and all the major events of the epic are recited by a character as either a first– or a second–hand account. Storytelling pegs the Mahabharata in the oral narrative tradition, but also gives a sense of the multitude of perspectives that necessarily shape the narratives of world-important events.
Deception
Deception is an interesting theme in the Mahabharata since there is no decisive ethical judgment on the matter. Instead, it is used by a tool of both dharma and adharma. When Duryodhana deceives Yudhisthira into gambling away his entire kingdom and even Draupadi's freedom during the dice game, this is clearly an instance of deception committed in sin. But when Krsna offers Drstarasrta an iron effigy of Bhima to maul so that he won't actually kill Bhima, this deception is carried out so that Drstarasrta does not impulsively stray from his dharma.