A fever (increase in body temperature) is often one of the first signs of illness. If your pet has a fever they are likely to be quieter than normal and probably will be off their food. If you check your pet's temperature and find it is raised then contact your vet for advice.
Any changes in your pet's behaviour, altered appetite or water consumption, or the presence of signs such as coughing or diarrhoea should alert you to the fact that there may be a problem with your pet. Most animals recover from illness in 24-48 hours - if your pet does not seem to be improving in this time or is getting worse then you should contact your vet.
Most owners can tell if their pet is limping or crying with pain, but it can be harder to see if your pet is suffering from a long-term discomfort such as arthritis. Dogs and cats generally show a change in behaviour or temperament when they're uncomfortable. A normally happy and affectionate pet may become grumpy and avoid human contact, preferring to sit or lie quietly by itself. If the animal can reach the painful area, they may lick, scratch, or bite at it.