Should one continue to exercise even when you are sick?
I know it may depend on the sickness, so I am specifically asking about minor things like a cold or fever?
Are there chronic sicknesses where you should still regularly exercise?
No, you should not exercise with with temporary illness such as a chest cold, flu, or fever. A runny nose or sore throat shouldn't prevent your exercise routine though. Once you have an infection or illness that effects your cardiovascular or digestive system, you should sit it out and let your body have the time needed to heal itself.
People with chronic ailments such as asthma, heart disease, and anything more serious needs to talk to their doctor before even thinking the word exercise. Some people can, some people can't even with the same symptoms. Your doctor will know best.