The rebels' advances coincided with new claims a government airstrike Sunday killed several children in a playground. Activists said at least 20 people died in Monday's violence a day after 97 others, including the playground children, were killed across the country.
Syrian Observatory for Human Rights said rebel forces had been attacking the dam's defenses on the Euphrates River for days before overrunning the facility Monday, The New York Times reported.
The dam supplies electricity to parts of Syria, the activists said, and is between the northern provinces of Raqa and Aleppo.
Information about the capture of the dam, as well as the capture of a military air base and other military facilities cannot be confirmed because of the government's restrictions on foreign journalists.
Rebels said they seized the military installations, including the Marj al-Sultan airfield, and 11 mobile anti-aircraft guns, in the latest of maneuvers in which forces against President Bashar Assad have captured facilities or seized weapons.
Rebels said government cluster bombs hit a playground in a Damascus suburb, killing the children, and posted a video, showing some of the dead and wounded, on the Internet.
Activists said the scene is near Dayr al-Asafir, near Marj al-Sultan.
Rami Abdulrahman of the Syrian Observatory for Human Rights, however, said it was not known what happened, CNN reported. The video couldn't be independently verified.
Among at least 20 people killed Monday were a woman and three children. Thirteen of the victims were reported in Damascus and surrounding areas.
Also Monday, fighting once again was reported beyond Syria's border, as insurgents reported Turkish anti-aircraft gunners opened fire on a Syrian government warplane that appeared to have entered Turkish airspace as it attacked rebel positions in the Syrian town of Atma, just across the border, the Times said.
The Syrian Observatory for Human Rights and the Local Coordinating Committees, as well as a fighter on the ground, said the Turkish fire prevented an attack on an area that includes a rebel headquarters and a camp for internally displaced Syrians.
Confirmation was not available, the Times said.
Turkey has requested NATO provide it with Patriot anti-missile batteries. Responding to criticism from Russia and others, Turkey's military Monday insisted the Patriot missiles would be used only to defend Turkish territory.
NATO experts were expected to begin an assessment of the 550-mile Turkey-Syria border to identify sites for possible bases and determine staffing and other technical details, the Times said.
About 40,000 civilians have been killed since the protests against the Assad regime began in March 2011, the opposition group, Center for Documentation of Violations in Syria, said. More than 380,000 Syrians have fled to other countries, the United Nations said.