I've heard of people letting their torts have the run of the house. Personally, I wouldn't do it because it seems so unsanitary, unless they were hatchlings or just a small tort... but even then I would keep them in their enclosure and not let them run around the house. Plus you can't potty train them.
Its not a good idea because they might eat something from the floor that could cause them a problem. Also, the floor is too cold for them. As an experiment, lay on the floor with no clothes on, and you'll see just how cool it is for you. The tortoise has no means to warm himself up. He requires the sun for that (or an expensive UVB light bulb). They are much better off inside their habitat where it is safe and warm. If you want a pet to ride a bike with you or tramp through the woods, or have running around the house, you might consider a cat or a dog.
j.martin, As the two have posted before me I agree I do not let my torts run around on the floors in my house. As Yvonne stated they might eat something that could cause them a problem and the floors are usually too cold for them. AsL BSKUNK stated it isn't very sanitary. Me I feel that not only for those reasons but because I am a cluts and may stumble and fall and squash or step on them. But I do take mine outside when the weather is nice and they love running around in the yard or in the pens I have made for the smaller ones. And even the hatchlings get time outside in a protable rabbit cage. Nothing better for most torts than the Sunshine. And nothing better for me than sitting watching them enjoy their time in it.
Even an enclosure sitting on the floor is usually too cold (that is why it is recommended to have it on a table or have legs on it). Agree with everything above. Sometimes I will take my tort and have him sit on my lap or in my hand for a few minutes on the couch, but only if he isn't looking scared. He seems to enjoy looking around. Gives me time to give him a good look over for his health while I hold him. Works well since he's small though.