In Saqlawiya in Anbar province, police beat off militants who tried to raid a police station, the New York Times reported. There were other clashes in nearby Fallujah.
The bombs claimed at least 64 lives, the Times said, including 18 people at the funeral in Diyala province. Most of the Baghdad bombs targeted markets, and all exploded during an hour in the morning.
The Middle East News Agency said the Baghdad bombs detonated in Shiite-majority or mixed neighborhoods.
In Mosul, officials said six other people, including three soldiers, were killed in attacks.
In Anbar province, meanwhile, Iraqi forces lost ground as Sunni gunmen, including those with ties to al-Qaida, stormed two areas when police abandoned their posts, MENA said.
Two children were killed and 13 other civilians were injured in sporadic fighting in Ramadi and near Fallujah that began Tuesday and continued into Wednesday, medical officials said.
The Iraqi government has been trying to reclaim territory from militants holding Fallujah and parts of Ramadi, the provincial capital.
"We gave ourselves up, and we gave up our arms" to al-Qaida-linked Islamic State of Iraq and the Levant, one police official told MENA.
"They have very heavy arms, which are much stronger than what we have," the policeman said. "Our police station was not very well protected, and they surrounded us. Even when we called for support, nobody came. Now, some of us have gone home, others have gone to other police stations."
Militants overran the police station in Saqlawiyah, west of Fallujah, and seized control after urging police to abandon their posts and their weapons.
The fighting in Anbar province began in December.
Rosie O'Donnell unveils nearly 50-pound weight loss
Putin thinks Obama would save him if he were drowning