Some of the aftermath was too horrifying to broadcast, reports CBS News Correspondent Tom Fenton.
"There were quite a few injured obviously. I saw one of the taxis, it literally flew and landed in front of the hotel," said eyewitness Ghulam Noor.
No group has claimed responsibility, but there are suspicions this is more than just another outbreak of India's Muslim-Hindu religious violence.
"This is probably the work of either al Qaeda or an al Qaeda-linked group," said M.J. Gohel, a leading expert on terrorism in Asia.
"These were simultaneous attacks, a sophisticated car bomb, and they chose soft-symbolic targets. Local groups would not act in this way; they tend to be more into rioting and looting and arson attacks," said Gohel.
And because the groups suspected of perpetrating this massacre operate out of Pakistan, there are wider implications.
India and Pakistan, both nuclear powers, were on the brink of war just last year. Now Pakistan, clearly worried that the Bombay attacks could push the countries back to the brink of war, was swift to denounce them.
"We deplore these attacks. We condemn all acts of terrorism," said Pakistan Foreign Ministry spokesman Massood Khan.
There could have been another purpose in the attacks. The United States has been urging a reluctant India to send troops to Iraq. If this is the work of al Qaeda, it could be a warning shot to India not to send them.
The timing of the blasts also raised concerns they were linked to a dispute over a religious site in the northern city of Ayodhya claimed by both Hindus and Muslims that has been the source of much bloodshed in the past. The bombings came hours after the release of a long-awaited archaeological report on the site that itself showed divisions over the site's history.
Ranjit Sharma, a police commissioner, put blame on Pakistan, saying suspicion in the blast fell on Islamic militant groups "let loose by the enemy country."
He specifically mentioned the Students Islamic Movement of India, or SIMI, a militant Muslim students' group outlawed in 2001, and Lashkar-e-Tayyaba, one of more than a dozen Islamic rebel groups fighting Indian security forces in Kashmir since 1989, seeking independence for the Himalayan province or its merger with Muslim-dominated Pakistan.
New Delhi accuses Pakistan of supporting militants, which Islamabad denies. Indian police said there was no direct evidence linking those groups, or Pakistan, to Monday's bombings.
The attacks appeared aimed more at the city of Bombay itself than at members of a particular religion.
One of the bombs exploded at the Gateway of India, a historic landmark and tourist attraction built by India's former British colonizers to commemorate the 1911 visit of King George V. The massive arch is often host to outdoor concerts and is a popular lunchtime eating spot for both Hindus and Muslims. The other blast was at the crowded neighborhood of jewelry stores, where many shops are owned by Hindus but where many of the artisans are Muslims.
"All kinds of people work here — Hindus, Muslims and Christians," said Ali Asghar, 24, a student whose father works in a bank near the jewelry market. "This is not about religion."
But his father feared Muslims would be blamed — and that anti-Muslim riots could follow.
"I don't want to leave Bombay. Where would we go? We feel safe here," said Mohammed Asghar.
Sushil Kumar Shinde, chief minister of Maharashtra, the state where Bombay is located, said the explosions had targeted the city's economy. "The blasts have thrown up a challenge to the resilience of this city," he told a news conference.
The death toll totaled 44 by early evening, Sharma said. Javed Ahmed, a police commissioner for Bombay, said at least 150 people were injured. Stock prices plunged after the blast reports. The benchmark index of Bombay Stock Exchange, the Sensex, closed at 4,005, down 119 points or 3 percent.
The blasts came just hours after the release of the archaeological report on the religious site in Ayodhya, where in 1992 Hindu mobs tore down the 16th-century Babri mosque, which they say was built on a temple marking the birthplace of their supreme god, Rama. More than 2,000 died in the nationwide violence that followed.
In March, a bomb attack on a Bombay train, which police blamed on Islamic militants, killed 11 people and wounded 64 others. That explosion came a day after the 10th anniversary of a series of bombings in Bombay that killed more than 250 people and were blamed on Islamic militants seeking to avenge Muslim deaths in the riots that followed the mosque's razing.
The report issued Monday by government archaeologists indicated there had been an ancient structure at the site, lawyers for both sides said, though they disagreed on whether it said there had actually been a temple.