ISIS claimed responsibility for one of the attacks.
The deadliest incident occurred in Baghdad's Sadr City, where a car bomb exploded, killing at least 24 people and wounding 71 others, according to security officials.
A bomb squad deactivated another bomb in a booby-trapped car in the same area, Iraqi television reported.
Two more explosions occurred in the al-Shaab neighborhood in northern Baghdad, killing at least 19 and wounding 44. A female suicide bomber may have been responsible for one of the blasts, the Interior Ministry said.
Finally, a suicide bomber detonated an explosive in a popular market in the Nahiyet al-Rashid neighborhood of southern Baghdad. At least three people died in that incident, according to security officials.
ISIS claimed responsibility for the al-Shaab attack in a statement on its Amaq news agency, SITE Intelligence Group said on Twitter.
No one had yet claimed the Nahiyet al-Rashid or Sadr City attacks, but the incidents come amid an uptick in violent attacks by the ISIS terror group in the country.
Prior to Tuesday's violence, ISIS attacks had claimed more than 100 lives in the past week.
At least 90 people died May 11 when several bombs went off in Baghdad neighborhoods. The next day, two suicide bombers attacked a police station in Baghdad, killing three officers.
On Friday, ISIS gunmen opened fire on a coffee shop in Balad
, a city about 80 kilometers (50 miles) north of Baghdad. That attack left 20 people dead.
And over the weekend, a car bomb killed two people in Latifiya located about 21 kilometers (13 miles) south of Baghdad, while 10 people died in explosions at a gas plant
in Taji -- just north of the capital city.
Experts have blamed the violence in part on a security vacuum they say has opened once again in Iraq as the country faces renewed political turmoil.
Prime Minister Haider al-Abadi is struggling to firm up a government capable of battling ISIS and, at the same time, address the country's long-standing economic and political wounds from years of war.
Terrorists have taken advantage of this vacuum to launch a fresh wave of deadly attacks, experts said.
A U.S.-led coalition has been pummeling ISIS targets with airstrikes. Two major Iraqi cities that had fallen to ISIS -- Tikrit and Ramadi -- have been reclaimed.
Iraq's government also has been planning a major offensive to recapture the northern city of Mosul, the largest city under ISIS control, and U.S. official
s and other analysts have said ISIS is lashing out as it loses ground.
"ISIS has receded somewhat militarily; they don't have a ... standing army to hold territory," political risk analyst Kirk Sowell told CNN
last week. "But what they're good at, unfortunately, is these terrorist attacks against soft targets."