When humans sit around all day, they can put on weight, and over the long term, health can suffer. It is no different for animals. This is why it is essential to take dogs for a walk. Cats get plenty of exercise outdoors, and by running around the house. Hamsters, and other rodents often have wheels (NEVER use a wheel for rabbits and guinea pigs, they break legs).
Rabbits and guinea pigs also need plenty of exercise. If they are outdoors, then they should be given a run for them to play in. This should be big enough for them to run a reasonable distance. For home based rabbits and guinea pigs, these are usually kept in a cage. However, a C&C construction can give them plenty of room to play in. The tools for this can be purchased online in places like eBay.
These animals are fine for allowing free run off the living room. They at pee and poo on the carpet now and again, but this is more an accident than habit. Besides, as they are herbivores, what comes out the backend is safe.
The best way to allow free run for these pets in the home is to setup the main living area, and a smaller area on the other side of the room. After a few days, they will tend to just run from one to the other. This is great fun to watch. Block off escapes for the first month, and hide wires. Once they have learnt what is ‘home and safety’ to them, these can then be removed.
Always make sure the animals are locked up when leaving the house, do not let them run free with no one there.