The Leonid meteor shower, the best views of which were to have been from Asia, was largely obscured by cloud.
The shower was caused by tiny high-speed particles from the tail of Comet 55 P/Tempel-Tuttle, which was last in the vicinity of the Earth in 1998.
Nasa had projected there would be up to 300 meteors raining down every hour.
On a typical night there are about eight per hour. In many of the viewing hotspots, however, hopeful visitors were let down by the weather.
Reports from the Philippines, Nepal and India were of cloudy conditions blocking a view of the night sky.
Schoolchildren in Sonipat, India, covered up to watch the shower
But there were a few stories of stargazing success.
Up to 1,000 people who camped out in a car park on the outskirts of Bangkok in Thailand spotted 52 meteors over several hours.
One group of amateur astronomers in India at the Siriska wildlife sanctuary, south of New Delhi reported counting 78 during a four-hour period.
"There was no moon in the sky, which is good for observation," Yogeshwar Kanu Aggarwal, a member of the Space Science Popularization Association of Communications and Educators, told the Associated Press news agency.
"We could see flashes of light for almost 10 seconds as bright as star Sirius."
North American observers stayed up from the early hours of the morning until dawn on Tuesday 17 November to view the shower's peak.