Too Few Inputs
Though a television may have multiple inputs, it may still have too few inputs to connect multiple consoles. For instance, you may have two HDMI output consoles but only one HDMI input on the television. A simple workaround is to use a compatible switch to artificially increase the amount of inputs to the television.
Wrong Input
A television may not have the correct input for a game console's output. For example, the television may only have a component video input while the console only has HDMI output. The solution in this situation is to use a video adapter, though not all types of outputs can be adapted to another form.
Older Television
If you have an older television with only one AV input, physically switching cables can cause a lot of wear and tear on the cables and input, eventually rendering them useless. In this case, use a switch that allows you to switch in between consoles without having to constantly change cables.