In a letter to his son Shaw Azim Shaw before his death he states: "I have a dread for my salvation, and with what torments I may be punished."
In a letter to his other son Prince Kaum Buksh he states: "I have committed numerous crimes, and know not with what punishments I may be seized."
Source: http://www.columbia.edu/itc/mealac/pritchett/00litlinks/txt_aurangzeb_lastletters.html
This is a somewhat complicated question to answer, as it requires an analysis not only of Aurangzeb's reign, but also of his notoriously complicated personal character. Aurangzeb is often considered the last of the great Mughal Emperors, and ruled during a time of significant Imperial upheaval. There are effectively two opposing characterisations of Aurangzeb, an older, more traditional characterization emphasizing his personal fundamentalism and intolerance as contributing to the decline of the Mughal Empire, and a more modern interpretation that presents a more nuanced version of Aurangzeb, presenting him more as a troubled, inadequate ruler, but not the fierce and brutal fundamentalist often presented. Both interpretations are not without their faults, and both are used by modern figures to advance certain political agendas, with the more traditional narrative often being espoused by the Hindu Nationalist community, and the modern narrative by proponents of secularism.
While I am not a fan of the traditional narrative, I have attempted to provide as much context for Aurangeb's "crimes" as I can, and have tried to present both sides of his character whenever possible. This being said, I am not a historian, and I strongly encourage anyone with more knowledge to contribute as well.
Most of the sources are from Abraham Eraly's "The Mughal Throne" and Audrey Truschke's "Aurangzeb: The Life and Legacy of India's Most Controversial King."
Born in Gujarat, Aurangzeb was the third son of then prince, and future Mughal Emperor Shah Jahan. As a young man, Aurangzeb was a deeply ambitious and dissatisfied student, not at all like his older and more popular brother Dara Shikoh. Dara was, as observed by his contemporaries, a studious and open minded individual; he was not particularly religiously orthodox, even by Mughal standards, and enjoyed learning for learning's sake. Aurangzeb, by contrast, once chastised his muhllah for not teaching him how to "besiege fortresses and fight pitched battles," lamenting the "idle and foolish" philosophies taught to him by his tutors (as recorded by Niccalao Mannuci, an Italian-born Mughal courtier).
As he grew older, Aurangzeb quickly found himself estranged from his father, Shah Jahan. Aurangzeb held a number of titles in his early years, deposed and once again reinstated as the governor of the Deccan, Aurangzeb also served as governor of Multan, and briefly participated in the disastrous Kandahar campaign. The Deccan specifically would prove to haunt Aurangzeb now and in his old age. In 1652, an accusation of embezzling money in Golconda would lead Aurangzeb to cease writing to his father altogether, communicating only through the official viziers from then on.
Aurangzeb was, as was first observed in the Deccan, an inherently humble person. Manucci oberseved that Aurangzeb always assumed "great humility of attitude," even accepting occassional disobedience from his officers, as he himself was "only a miserable sinner" who everyday "neglected and repudiated" orders from God. Yet, despite this personal humility, Aurangzeb was also extremely skilled in the art of politics and deception, once writing that it was "contrary to the Quran to consider stratagem as blamable." Indeed, Aurangzeb often developed theological justifications for his ambition, believing very strongly that success came only to those who followed in the footsteps of the divine. To Aurangzeb, temporal success was a measure of right and wrong; success could, as far as Aurangzeb was concerned, never come to those who disregarded the lord. Accordingly, Auranzeb devoted his life to upholding Islamic doctrine, he spurned music and poetry as hedonic pleasures, and spent most of his time managing his vast empire. Both in the Deccan and later as emperor, Aurangzeb hesitated to apportion his power, few Mughal nobles shared his orthodox beliefs, and many could prove a threat to his reign if giving enough influence.
Aurangzeb and his brother Dara fell into a significant power struggle following the ilness of Shah Jahan in 1657, and it is with this that we may begin seriously compiling Aurangzeb's "crimes." The details of the struggle are not particularly important in understanding Auragzeb's quote, the truly important development of this conflict was that Aurangeb won. Following this victory, Aurangzeb had Shah Jahan imprisoned in Agra, and, in 1659, ordered Dara executed. Aurangzeb was now emperor.
As emperor, Aurangzeb endeavoured to follow the Shariah as closely as possible, and this included, most infamously, the destruction of Hindu temples. Aurangzeb's first actions to this effect were in Benares (Varanasi), where he issued a firman ordering a ban upon "new temples" in the area. Critically, Aurangzeb did not yet order the destruction of old temples, only a prohibition upon new constructions. Indeed, when informed that officials had disturbed older constructions, he ordered that "no person shall in unlawful ways interfere with or disturb...Hindu residents in those places." Over time, Aurangzeb's measures hardened, In 1669, Mustaid Khan reported that Aurangzeb instructed "all governors...to destroy with a willing hand the schools and temples of the infidels," in 1670 "several cart loads of idols" were transported to the steps of the Jama Masjid "for being todden upon." In the same year, Mannucci writes that Aurangzeb ordered his governors to "never again" allow "a woman to be burnt." (abolishing sati). While previous Mughal emperors (including the tolerant Akbar) had destroyed temples as well, Aurangzeb made such destruction a clear royal policy.
Regardless of his personal feelings, the state of his empire forced Aurangzeb to be a pragmatist. Hindu Rajputs served on in the Mughal army, and continued to hold noble ranks. Aurangzeb's own minister of finance was, for a time, a Brahmin. By the end of his reign, Aurangzeb would employ more Hindu bureaucrats than any of his predecessors.
In 1679, Aurangzeb imposed one of the most infamous decrees of his reign (although it has been somewhat overshadowed by his temple policy today), he reimposed the Jizya. According to Manucci, the Jizya was extremely unpopular, even within the Mughal court, unpopular enough for "all important men to oppose themselves to this measure." While Manucci's claim is no doubt exaggerated, it is enlightening nonetheless. Even Jahanara Begum, Aurangzeb's older sister, is said to have protested, comparing India to a sea, and her fellow Mughals as small ships, pleading with Aurangzeb not to "disturb the seas."
Despite the fears of his advisors, Aurangzeb's taxation did not immediately lead to wholesale rebellion, however it can certainly be argued that such policies did stoke the fires of discontent throughout the empire. This, combined with the economic stagnation of the empire and Aurangzeb's quickly widening campaigns in the Deccan, led to a breakdown of Mughal rule. Slowly, the empire began breaking into rebellion.
The details of these rebellions could fill an entire book, and indeed many books have been written about the rebellions of the late 17th century. Ultimately, minute details are not particularly necessary to understand the context of Auranzeb's quote, a quick summary will suffice. The first major rebellion occurred near Mathura, where Hindu Jats temporarily established their own kingdom. In 1672, a rebellion of local Pashtun leaders near Kabul led to an almost complete decline in Mughal authority near the Khyber. In 1699, Sikh leaders in Punjab rebelled following the execution of the Sikh Guru Tegh Bahadur. Most importantly, the Mughal-Maratha wars began in 1657, with Aurangzeb's continued expansion into the Deccan. These wars would continue until Aurangzeb's death, with successive Maratha leaders continuing to harass Aurangzeb until his death. By the 1760s, 50 years after Aurangzeb's death, Maratha armies would reach as far north as Delhi, looting the Mughal Durbar in 1761.
It was with these developments that, in 1707, upon his deathbed, Aurangzeb looked upon a dying empire. Having succeed Shah Jahan, Aurangzeb had began his reign at the empire's military and economic climax, by 1738 (only three decades after his death), Persian ruler Nader Shah would loot Delhi, stealing the famous peacock throne. Manucci writes that the Deccan was, by Aurangzeb's death, "devoid of trees and bare of crops," with "over a hundred thousand" annual deaths in the Mughal army since the beginning of hostilities. In his dying weeks, Aurangzeb, himself a veteran of a succession crisis, tired to ensure the peaceful transition of empire, ordering his heirs to all corners of the empire. Humbly preparing for his funeral, Aurangzeb instructed his chief Kazi to "consign him to the earth without any useless coffin."
In his final letter to Azam Baksh, Aurangzeb wrote "I have not done any governing of the realm or cherising of the peasentry...I have brought nothing with me, and am carrying away with me the fruits of my sins...of the future there is no hope." Aurangzeb, devout as ever, believed that he had failed, failed to uphold the will of the heavens, failed to deliver victory to his empire, and ultimately, failed to expand and safely deliver his empire to his successors. To Aurangzeb, his was the crime of failure.