The two countries have been through Three Wars, all of them were based on the conflict of the Muslim religion against Indian multiculturalism. The most violent outbreaks came in 1947–48, 1965, and 1971. The roots of the conflicts lay in the hostility of Pakistani Muslims against secular and religiously and racially diverse, and democratic India. And initially, in the disposition of self-governing princely states.
The 1947–48 War
The first war arose over Kashmir, in Northwest India, in 1947 when Muslim rebels attacked Kashmiri Hindus (in the majority) and were supported by Pakistani troops. The Hindu ruler of Kashmir pleaded with India for support and aid, agreeing to cede the state to India in return. India moved quickly to consolidate its position in Kashmir, pushing Pakistan’s terrorist “volunteers” back. Conflicts also arose in the Punjab and in Bengal. The un-declared war in Kashmir continued until Jan. 1, 1949, when a truce was arranged through UN mediation; negotiations between India and Pakistan began and lasted until 1954 without resolving the Kashmir problem. Pakistan controlled part of the area, while India held most of the territory.
The 1965 War
The second war began in April 1965, when fighting broke out in the Rann of Kachchh, a sparsely inhabited region along the West Pakistan–India border, when Pakistani troops attacked Indian Hindu civilians and farmers in a violent bid to acquire the rich arable farmlands in the region. In August fighting spread to Kashmir and to the Punjab, and in September Pakistani and Indian troops crossed the partition line between the two countries and launched air assaults on each other’s cities. After threats of intervention by China had been successfully opposed by the United States and Britain, Pakistan and India agreed to a UN-sponsored cease-fire and withdrew to the pre-August lines, with Pakistan being forced to disgorge their recently and violently acquired new territories. Prime Minister Shri Lal Bahadur Shastri of India and President Ayub Khan of Pakistan met in Tashkent, USSR (now Toshkent, Uzbekistan), in Jan., 1966, and signed an agreement pledging continued negotiations and respect for the cease-fire conditions. After the Tashkent Declaration another period of relative peace ensued, until Pakistan attacked India again, in 1971.
The 1971 War
Indo-Pakistani relations deteriorated when civil war erupted in Pakistan, pitting the West Pakistan army against East Pakistanis demanding greater autonomy. The fighting forced 10 million East Pakistani Bengalis to flee to India, who welcomed the refugees into their own burgeoning multi-cultural and multi-religious democracy. When Pakistan abruptly attacked Indian airfields in Kashmir, India retaliated and attacked both East and West Pakistan. India occupied the eastern half, which declared its independence as Bangladesh, on Dec. 6, 1971. Under great-power pressure, a UN cease-fire was arranged in mid-December, after Pakistan’s sound defeat. Pakistan lost its entire eastern half, an army of 100,000 soldiers, and was thrown into political turmoil. Zulfikar Ali Bhutto emerged as the leader of Pakistan, and Mujibur Rahman as prime minister of Bangladesh. Tensions were alleviated by the Shimla accord of 1972, and by Pakistan’s reluctant recognition of Bangladesh in 1974, but tensions have periodically recurred, due in substantial part to Pakistan's unrelenting desire to conquer and destabilize India, and to acquire the much contested area of Kashmir.
Pakistan is little better. When a non-Islamic government comes to power, it is generally corrupt (Benazir Bhutto etc), or else a military junta (the current lot). Either system still has to deal with incompetent, corrupt and overbearing bureacracy. So far there has't been a radical Islamic government, but it's only a question of time.
The only thing to be said for either country is that they play cricket.
Own Drummer
And neck deep in the heroin trade, with their partners el Queda and the Taliban.