Some 39 people, including five children, were killed and 35 injured in Ujjain in Madhya Pradesh state as a crowd of devotees tumbled over each other down a narrow staircase inside a temple complex.
Most of the victims died of suffocation. A few were gored by bamboo and steel wires as they were thrown against a temporary barricade which had been erected around the main area of worship inside the temple.
Twenty-one others, including 18 women and one child, were killed and 40 seriously injured when devotees rushed to bathe in the River Ganges at the holy northern town of Hardwar.
Eyewitnesses in both towns blamed the authorities for the accident, saying precautions to prevent crowd surges were inadequate.
Officials said dozens of the 200,000 devotees at Ujjain were trampled underfoot as they raced down marble steps to a temple.
Thousands of devotees, mostly farmers, had gathered on Sunday night to ensure early entry into the temple.
"It's tragic. Most of them had come to thank God for the rains," said the Ujjain commissioner, PS Tomar.
"Several of them were seen dancing and singing in praise of God as they queued up in front of the temple gates," he said.
Some devotees carried on with their rituals until evening, but most of Ujjain's residents were in shock.
In the incident at Hardwar, the 21 victims were crushed to death in a stampede on an overcrowded bridge, which was being used by more than 2 million devotees who had gathered to take a dip in the Ganges river.
The often frenzied worship by throngs of Hindus has led to tragedies in the past. In 1992, a stampede in the southern town of Kumbakonam during a religious holiday killed 50 people.
The worst stampede recently was two years ago at a demonstration in Nagpur of tribespeople demanding job quotas. About 120 people were killed and 500 injured when police tried to break up the demonstration.