A BBC reporter said he'd seen black smoke pouring out of one of Saddam Hussein's presidential palaces in the city.
The US Defence Secretary, Donald Rumsfeld said: "The [Iraqi] regime is starting to lose control of their country."
Mosul, the main city in northern Iraq, was among the targets.
And large explosions were reported in the northern oil centre of Kirkuk.
Other main points:
Two US marines were killed in southern Iraq, hours after eight British and four American servicemen die in what was believed to be a helicopter accident
Eight American B52 bombers took off from a British airforce base in the west of England, thought to be heading for Iraq.
An American convoy which has raced north across the desert from the Kuwaiti border has reached the outskirts of the Iraqi city of Nasariyah - roughly a third of the way to Baghdad.
Protests against the war in Iraq have taken place in many countries, including Egypt, Malaysia, Italy and Jordan.