Gems, minerals, rocks and meteorites: 350,000 minerals, 17,000 meteorites, 127,000 rocks and 10,000 gems
Amphibians and reptiles: 570,000 specimens, the world's largest collection
Mammals: 590,000 specimens, the world's largest collection (and nearly twice the size of the second largest)
Birds: over 640,000 specimens, including representatives of about 80 percent of the world's known bird species
Fish: 4 million specimens, the world's largest collection
Invertebrates (except insects): 35 million specimens from around the world
Entomology: the National Insect Collection, housing 35 million specimens in more than 5,200 cabinets
Paleobiology: 40 million fossil animals, plants and single-cell organisms (and sediment samples) including 1,500 dinosaurs
Add in the anthropology collection and you find that the National Museum of Natural History cares for more than 126.6 million objects and specimens---the world's largest and most comprehensive natural history collection. And it keeps growing.
As we can see from the entomology research, these items are collected not just for the sake of having something unique or different. They support important research, from learning about how to prevent birds from striking airplanes to how the human species evolved, and the teaching of new scientists. I'm in awe.