Regular exercise is important to keep all animals healthy. Most cats are good at regulating their exercise and match their food intake to their energy needs; dogs are less good at this.
If your pet is showing signs of stiffness when they get up from rest they may be getting arthritis. If so the exercise programme should be altered accordingly. Regular short walks will allow your pet to maintain mobility better if they are arthritic. If your pet is overweight then a diet may help improve its condition and allow it to exercise better.