The bombing at the cafe in Baghdad's primarily Shiite Amil neighborhood happened as it was full of customers. The cafe and a nearby juice shop is a favorite hang out in the neighborhood for young people, who filled the area at the time of the explosions.
The blast killed 35 people and wounded 45, Iraqi officials said.
Violence has been on the rise in Iraq following a deadly crackdown by security forces on a Sunni protest camp in the northern town of Hawijah in April. At least 385 have died in attacks in Iraq so far this month, according to an Associated Press count.
In a village north of Baghdad, a car bomb targeted a police officer's house, killing his father, brother and five nephews, officials said. Six others were wounded in the blast, which happened when the officer was not at home.
Security forces meanwhile foiled an attack on the local council of the western town of Rawah by five would-be suicide bombers disguised in police uniforms, said Muthana Ismail, head of the local security committee.
Ismail said two attackers were shot while the rest blew up themselves up outside. Two police officers and an official were killed, while 20 people were wounded, he said.
Rawha is about 330 kilometers (200 miles) northwest of Baghdad.
There was no immediate claim of responsibility for Sunday's attacks, though car bombings and gun assaults are favorite tactics of al-Qaida's local branch. It frequently targets Shiites, whom it considers heretics, and those seen as closely allied to the Shiite-led government in Baghdad.
Hospital officials confirmed the casualty figures for all attacks. All officials spoke on condition of anonymity because they were not authorized to speak to journalists.
Associated Press writers Sinan Salaheddin and Qassim Abdul-Zahra contributed to this report.