These observations make Saturn's rings the only location besides Earth, the Moon and Jupiter where scientists and amateur astronomers have been able to observe impacts as they occur, Nasa said.
Studying the impact rate of meteoroids from outside the Saturnian system helps scientists understand how different planet systems in our solar system formed.
The solar system is full of small, speeding objects. These objects frequently pummel planetary bodies. The meteoroids at Saturn are estimated to range from about one centimeter to several meters in size.
It took scientists years to distinguish tracks left by nine meteoroids in 2005, 2009 and 2012.
Results from Cassini have already shown Saturn's rings act as very effective detectors of many kinds of surrounding phenomena, including the interior structure of the planet and the orbits of its moons.
For example, a subtle but extensive corrugation that ripples 19,000 kilometres across the innermost rings tells of a very large meteoroid impact in 1983.
"These new results imply the current-day impact rates for small particles at Saturn are about the same as those at Earth - two very different neighbourhoods in our solar system - and this is exciting to see," said Linda Spilker, Cassini project scientist at Nasa's Jet Propulsion Laboratory in Pasadena.
"It took Saturn's rings acting like a giant meteoroid detector - 100 times the surface area of the Earth - and Cassini's long-term tour of the Saturn system to address this question," Spilker said.
The Saturnian equinox in summer 2009 was an especially good time to see the debris left by meteoroid impacts. The very shallow Sun angle on the rings caused the clouds of debris to look bright against the darkened rings in pictures from Cassini's imaging science subsystem.
"We knew these little impacts were constantly occurring, but we didn't know how big or how frequent they might be, and we didn't necessarily expect them to take the form of spectacular shearing clouds," said Matt Tiscareno, lead author of the study.
"The sunlight shining edge-on to the rings at the Saturnian equinox acted like an anti-cloaking device, so these usually invisible features became plain to see," he said.
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