changing wire guage over distance?

I sometimes find myself changing the guage of a wire between the power source and the device. For example, at the source the wire will be let's say 16g but the connector to the device will only fit an 18g or 20g wire, so I connect the 16g and 18g wire together since for whatever reason the 18g was not the right size to connect to the power source. Will this change in gauge size affect current or the voltage traveling across the two wire sizes from power source to device?

As long as the smaller wire is able to handle the current demands of the circuit, there will not be a problem.

And the power source end fuse suits the smallest cable.... It is done quite often as a mean of reducing overall resistance/voltage-drop. EG - you may only need 18G, but use 16G or larger as far as you can for lower losses. But the fuse upstream of the 18G should suit the 18G (whether it be between the 18G and larger cable, or at the beginning of the entire run).