No one has claimed responsibility for the bomb blasts. Assam has been a focus of a separatist insurgency for decades, but it has also recently suffered bomb attacks blamed on Islamist militants from neighboring Bangladesh.
Many of Thursday's blasts were in crowded markets in the state and many bombs were hidden in motorcycles or scooters.
Firefighters doused the smoldering remains of cars and motorcycles at one of the blast sites in Guwahati. One of the blasts targeted a high-security zone with a court as well as offices and the homes of senior police officials.
Television channels showed some people lying on the streets, their clothes soaked in blood. Some of the walking wounded were helped into ambulances by local people and police.
"Immediately after the blast there was complete darkness for a while and I later saw several bodies and severed limbs all around," said Bikash Goyal, a witness in Guwahati.
Twenty-nine people were killed in four blasts in Guwahati and the remainder in the other three towns in the state, according to a spokesman in the office of Assam's chief minister.
A wave of bomb attacks has hit India in recent months, killing more than 125 people. Police have blamed most of those attacks on Muslim militants, although some Hindu militants have also been suspected of carrying out several attacks.
Security analysts and military intelligence officials said the Assam blasts bore hallmarks of strikes by Islamist militants.
"These blasts look like the handiwork of terrorist groups from Bangladesh, as you need sophisticated militant groups to carry out such coordinated attacks," Major General Ashok Mehta, a security analyst, told Reuters in New Delhi.
"It is quite possible that separatist groups are not involved at all," Mehta added.
The United Liberation Front of Asom (ULFA), Assam's major separatist group often blamed for attacks, denied involvement.
The attacks were condemned across South Asia.
"I am confident that the people of India will rise unitedly against these attempts to disturb peace and harmony and to destroy our social fabric," Indian Prime Minister Manmohan Singh said in a statement.
Pakistan, often blamed by New Delhi for fomenting trouble in neighboring India, condemned the attacks and called for international cooperation to tackle strikes by militants.
PACKED BUS BURNED
Pankaj Goswami, a witness at a blast in Guwahati, said: "The impact of the blast was so huge, a packed bus got half burned and we pulled out a lot of injured people and sent them to hospital."
Local television said a curfew was imposed in Guwahati after angry crowds attacked police and set cars on fire. Police fired in the air to disperse the angry mob.
In October, at least two people were killed and 100 injured in four bomb blasts in Assam that police blamed on Muslim militant groups based in neighboring Bangladesh.
Last month, Assam state was also hit by clashes between indigenous tribes and Muslim settlers that killed at least 47 people.
Ringed by China, Myanmar, Bangladesh and Bhutan, India's northeast is home to more than 200 tribes and has been racked by separatist revolts since India gained independence from Britain in 1947.
Local citizens accuse New Delhi of taking away the region's mineral and forest resources, neglecting development and allowing in a flood of outsiders.