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The two bombs, planted in taxis, went off during the lunchtime period.
One exploded at the Gateway of India, the city's top tourist attraction.
Witnesses said the blast left trails of blood in front of the Gateway, a colonial arch built next to the sea and one of India's most famous landmarks.
The taxi containing the bomb was parked outside the Taj Mahal Hotel, one of the city's oldest luxury hotels, where windows were shattered and cars damaged.
The force of the explosion is reported to have thrown several people into the sea.
There were scenes of even worse carnage at the site of the second car bomb, in a busy jewellery market near the Mumba Devi temple in central Bombay.
The bomb exploded in front of a multi-storied building containing shops on the ground floor and flats above.
"You can't imagine what I saw. Bodies strewn around. I was in my flat when I heard a deafening sound. The building shook from its foundation," local resident Prashant Zaveri told the BBC.
BBC correspondent Zubair Ahmed says pieces of broken glass, blood stains and smashed cars and shops could be seen for 100 metres around the spot where the blast took place.
Pakistan-based groups blamed
It is not yet known who carried out the attacks, although it has been hinted that outlawed student Islamic groups could be involved - particularly the Pakistan-based militant group Lashkar-e-Toiba.
The people of Delhi blame the Kashmir rebel group for the December 2001 attack on their parliament which left 15 people dead, including the five gunmen who carried out the raid.
Following that attack, Pakistan and India came close to war, but relations are now improving.
Pakistan has been quick to condemn today's bomb blasts.
"We deplore these attacks," said Foreign Ministry spokesman Masoon Khan. "We condemn all acts of terrorism and I think that such wanton targeting of civilians should be condemned in the strongest possible terms."
It has also been suggested that the blasts may be linked with the release of a report on the controversial religious site at Ayodhya. The dispute has been blamed for previous explosions in Bombay.
The final casualties in the bomb blasts were put at 52 dead and 150 injured.
Four men and a woman were charged in June 2004 under India's tough Prevention of Terrorism Act with conspiring to explode the two car bombs and an earlier bus bomb in July 2003.
They are accused of working for Kashmir militant group Lashkar-e-Toiba to build and detonate the bombs. All deny the charges.
Another suspect, said to have been the mastermind behind the attacks, was killed in a gun battle with police in September 2003.
The day after the blasts, Delhi demanded that Pakistan handed over 19 suspects wanted in connection with other attacks.
Pakistan denied giving shelter to any such suspects.
However, the impetus for a rapprochement between the two sides has been maintained, and in June 2004, India and Pakistan held two days of talks focusing on the Kashmir dispute, which they described as "positive".
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