For Mudflows
The Osceola Mudflow happened 5,600 years ago and was a signature event of Mount Rainier's, it happened during the Holocene.
bibliography:http://volcanoes.usgs.gov/volcanoes/mount_rainier/mount_rainier_geo_hist_79.html
For Lahars
Prior to the Osceola Mudflow that happened 5,600 years ago, three lahars happened, each first being a avalanche that included changed rocks, swept down the south side of Mount Rainier.
bibliography:http://volcanoes.usgs.gov/volcanoes/mount_rainier/mount_rainier_geo_hist_79.html
For Landslides
Happened in a remote area of Glacier Bay National Park, the slide was so big it came up on the earthquake monitors as a magnitude of 3.4 event. Even though it did not have a name it was still major landslide.
bibliography:http://usnews.nbcnews.com/_news/2012/07/13/12722446-5-mile-long-landslide-in-alaska-national-park-warming-eyed-as-possible-culprit?lite
For Avalanches
On 31 May 1970, an earthquake off the coast of Peru caused a large section of the north slope of Mt. Huascaran to collapse. The avalanche moved down hill at a speed of 100 miles per hour with a mass of roughly 80 million cubic feet of ice, mud and rock. It ran nearly 11 miles, burying the towns of Yungay and Ranrahirca in up to 300 feet of rock and debris. Estimates suggest that the earthquake killed over 20,000 people.
bibliography: http://unofficialnetworks.com/largest-avalanche-20000-killed-75833/