Most of our rats have been free-range. They do have a cage but their door is always open (but we do have to have a couple of litters trays in each room, and you have to be careful to keep cables protected or out of reach, and not leave clothes laying around). Some keep to themselves a little more than others, some insist on not only coming to bed with us but really snuggling up. Most will come if you call them and/or russle food.
Some have perfect recall, so I sometimes let them play outside - but only one at a time and never out of my sight.
Occasionally, one will go "missing" - in that I might not have seen them all day and I start to get worried, but they've usually just fallen asleep in an atypical place.
We did, once, have a pair of rats where one was a real explorer. She was very obedient if you were there to supervise (great recall, knew a few tricks) but she was a climber and always wanted to investigate new spaces. We left her and her sister unattended on one occasion, for about 15 minutes, and came back to find she had chewed a hole into the wall (well, widened the existing hole where radiator pipes) and disappeared into it. She immediately came back when called.
I also inadvertently left the patio door slightly ajar one day, but only for a moment. I closed it promptly and went off to work. DP was home and, an hour or so after I left, there was ratto at the door, wanting to be let back in.
She and her sister were, by necessity, the only ones that we had to keep caged while overnight and when we were out.
Most, though, just lounge around or get up to harmless mischief.