The New Museum’s summer show “The Keeper” explores the complex relationships we have with the things we collect. Why do we amass certain objects? How do these collections affect us and those around us? When does a pleasant hobby cross the line into obsession, even madness?

Inspired by this vast exhibition, which includes some 4,000 items and artworks over four floors, created or preserved by 30 “keepers,” The New York Times asked readers to submit stories and photos of their own collections. The hundreds of responses were inspirational, delightful, poignant, shocking and disgusting, occasionally all at once. A sampling of these collections:

Absolut Vodka ads. Apple stems. Avocado seeds. Beach plastic. Branded barware. Broken objects. Chopstick wrappers. Discarded snapshots. Doll heads (“The head must be found as a separate item,” wrote Brenda Segel of New York.) Donald Duck memorabilia. Egg cups. Goddess statues. Greeting cards. “Harry Potter” books in different languages. Hotel room keys. Lucite grape clusters. Mah-jongg sets. Marijuana tax stamps. Men’s polyester disco shirts. Museum toilet paper from Europe. Nirvana posters. Oyster shells. Pockets. Potty-training books. Rubber ducks. Sand. Skull mugs. Soviet watches. Troll dolls. Typewriters. Vintage: Barbie structures, electric clothes irons, figures of the Virgin Mary, handkerchiefs, metal measuring tapes, photos of a baby and a dog in a playpen, photos of people and places named Dick, Thermoses, Western Electric telephones.

The word “hoarder” came up more than once. Some readers expressed a tinge of regret; many more, joy. And a few, befuddlement. “It started out innocently enough with a plastic banana in a Ziploc bag on the door of my apartment when I was in college,’’ wrote Scott McCarney of Rochester. “Before I knew it I was publishing a newsletter and collecting bananabilia.”

Here are some of our favorite reader collections, with explanations edited for space. “The Keeper” runs through Sept. 25.