Neely was a kleptomaniac, she would fill her pockets with every conceivable item in the house. The bathtub strainer kept disappearing until we heard a strange noise coming from the bathroom one day and found her in the tub taking it out.
Carleton, on the other hand, is a love bug and would fill his pockets with kisses if he could.
My cats have been collecting these sticky balls from some kind of bush. I already pluck off like 15 a day, so they'd probably store even more! Besides that hair ties, treats, receipts, shoe laces, anything they can play with really.
Flora would have things she's collected throughout the day. Remy would have a list of ways to kill the dog. Maisie would have food crumbs because she wouldn't have anything left.
Corn kernels and my mini laser pointer. Juno's figured out where the red dot comes from but not so much that she can't bring it forth herself. And she's a fiend for fresh corn kernels. I only give her a couple when they're on hand but I suspect she'd stuff her pockets with more if she could.