The time someone needs for a connection varies from one airport to the other and from one flight to another. Usually with a domestic flight it can go from half an hour to one hour, and for international flights it can go from one hour to three hours. Most of the times that you are making a connection the gates are next to each other or in close proximity to avoid any missed flights. As in anything there are exceptions to the norm.
There are times where the connection times are very important such as when you are connecting to different airlines, or traveling internationally. When connecting from one airline to another it can take more time if the gates are not in the same terminal and therefore require a longer connection time. International flights that require you to go through customs usually require longer connection times also.
Most airlines will offer multiple connections so if you feel you need more time you can purchase a flight with a longer connection. When an airline sells its flight it takes into consideration the connecting time and will only sell flights that give you enough time to connect.