Axis plays an important part in making sense of a visualization. Oftentimes, it's important to follow the "zero rule" (the axis starts at 0). There are times, though, where it is required to modify the axis to suit our purpose. It can also vary depending on the choice of visualization.
In bar chart, if we truncate the y-axis, it could mislead the viewers. In such cases, even the small difference across categories could look like a big difference. However, 'zero rule' may not necessarily apply to other chart types including line chart.
Although the axis is not clearly pronounced in pie chart, it is generally recommended to start the slices from either 0 or 90 degrees, in order to make a pie chart easy to read.
It is extremely important to keep the axes same in small multiple. Not keeping it same would hinder the inference capabilities of viewers and would most likely result in wrong insights. In this case, both should have started from 30 or 40.
Back to back
Here, it is difficult to compare across categories in back to back chart. It could have become easier to gather insights if the categories on the y-axis were arranged in either ascending or descending order.
Make sure that the Y axis starts with zero; otherwise, the relative distance between the categories could be skewed.
In case of boxplots, one can break away from "zero rule"; otherwise, the boxplots could look skewed and it could be difficult to compare summary statistics.