The blasts hit government-held Tartous and Homs, as well as Hasakeh, which is mostly controlled by Kurdish forces but where the Syrian government maintains a presence, AFP reported.
State media said at least 11 people had been killed and 45 injured in a double bomb attack just outside the city of Tartous, in the coastal province of the same name, which is a stronghold of Syrian President Bashar Assad's government.
"Two terrorist blasts on Arzuna bridge, the first a car bomb and the second a suicide bomber who detonated his explosive belt when people gathered to help the wounded," state television said.
State media also reported five people killed in Hasakeh, in the northeast of the country.
The so-called Syrian Observatory for Human Rights, a Britain-based group, said the blast hit a checkpoint belonging to the Kurdish Asayesh security forces.
And state media also reported a car bomb at the entrance to the Al-Zahra neighborhood in central Homs city, which is controlled by the government.
It said at least two people were killed and four wounded in the bombing, which is the latest in a series of attacks targeting Al-Zahra neighborhood.
State media also reported another bomb attack on a road west of the capital Damascus, but gave no immediate toll in the blast.
The Observatory said that attack targeted a checkpoint and gave a toll of three dead.