I'd love to provide my rabbits with a mound of dirt they can dig in as much as they want, but it isn't always possible. Their wild cousins (Oryctolagus cuniculus) in the UK and elsewhere dig large warrens. These warrens provide the rabbits with underground passages that are deep enough to provide shelter and protection from predators. The warren passage openings are used for daily comings and goings and some are mainly "bolt-holes" if there is danger nearby. The tunnels themselves average 9 inches wide and there are main runs which lead to areas above ground to graze.
My rabbits live in a safe environment inside my home so they basically live in my human warren. (sometimes I wonder if it isn't the reverse). Even though they have a big area to run in and live, they still enjoy a nice narrow tunnel to run through for play and sit in part of the day. Over the years I have provided my rabbits with amazing habitats, but when it comes down to it, they like a long dark tunnel. Go figure. I started out years ago with cardboard cement forms in tube shapes from hardware stores. They were coated with something on the outside and fortunately the bunnies never chewed it. Now there are plenty of nice cardboard tunnels available (see all the online outlets below) and even habitats with short passages. I bought a fabric tunnel for the cats from Ikea recently and even though my rabbit Pansy has plenty of places she could relax, she has claimed it as her own (pictured). I'm lucky she is not a fabric chewer. The cats are stuck with their cat trees and I'm sure Pansy would agree that's where they belong.
The Blissful Bunny
Best Little Rabbit, Rodent & Ferret House
Bunny Bazaar (UK)
Cats and Rabbits and More
Pet Care Depot
Pluesch Nasen (Plush Noses) A German website