Thickness (cross sectional area of the wire), length, and temperature all have some effect on the amount of resistance created in a wire. Another factor is the conductivity of the material we are using. Some metals are just more electrically conductive than others. As long as I use the same type of metal for each wire, my experiment will remain fair.
Cross Sectional Area
The thicker the wire, the less resistant it is. This is because there are more electrons in the metal that are free to move as a current. Also, there is more space for the electrons to flow, so more can fit down. This is often compared to water in a pipe; the thicker the pipe, the more water that can flow through it.
The temperature of the wire also affects the resistance. This happens because as the metal gets warmer, the metal ions in the wire gain kinetic energy and start to vibrate. As their motion becomes more erratic they are more likely to get in the way and disrupt the flow of the electrons and therefore increase the resistance.
Length of the wire
This is easier to explain using the "hallway" analogy. Imagine in a corridor, there are some people (electrons) trying to move, and there are some people (ions) staying still. If the corridor was very short, there is a high chance that the "electrons" will make it to the end. If the corridor is very long, there is more chance of the "electrons" colliding with an "ion" and therefore decreasing the amount of current.