The attacks came as many shoppers were out buying new clothes in anticipation of the Eid al-Adha holiday, which begins in about a week.
"It was a busy time for shopping, so there were a lot of people around," said Ahmed Naseer, the owner of a stationary shop nearby. "When I came out, I saw burning carts and merchant stalls, and children crying and women screaming out of fear. The whole place was full of panic."
Earlier in the day, gunmen opened fire on a police patrol in the Shiite neighborhood of al-Shaab, killing two policemen and wounding another.
Authorities also said gunmen shot dead a police lieutenant colonel who worked with the State Identity Directorate late Friday in the capital's Karradah district.
Hospital officials confirmed the deaths in the Baghdad attacks.
Near the northern Iraqi city of Mosul, gunmen attacked a police checkpoint and killed three officers, according to two police officials.
Gunmen also shot and killed a prison official in a drive-by-shooting during the morning rush hour in eastern Baghdad, said Justice Ministry spokesman Haider al-Saadi.
Violence has ebbed in Iraq since the peak of the bloodletting in 2005-2008, but insurgents still frequently attack predominantly Shiite areas, government officials and security forces in an attempt to undermine the Shiite-led government.
Saturday's attacks marked Iraq's deadliest day since Sept. 30, when a string of coordinated blasts that hit Shiite neighborhoods and struck at Iraqi security forces left at least 26 dead.