Scientific figures are usually messy enough, there’s no need to aggravate the problem by including redundant labels. As with figure captions, problems arise with multi-panel plots. If the panels share axes, there’s no need to label each one.
Repeating labels causes several problems: it adds unnecessary detail, it makes the link between panels less obvious, and it cuts into the whitespace available.
Consider the following example showing the relationship between three quantities.
Here’s the improved version:
Scientific figures can easily contain far more than three panels. The number of unnecessary labels adds up quickly.
An actual example
I leave you with an example based on an actual figure from an article published in a well-known, reputable journal. The important aspect of this figure is the differences between models. However, these differences are difficult to discern because the individual plots are so small as a result of unnecessary repetition.
There are several problems with this figure (e.g., the jet colourmap and a colourbar without a label), but I’ll focus on the repeated labels. Clearly, there’s no need to repeat the 90°W and 90°E labels on every panel. All this does is reduce the amount of space left for the map. You can also note that “Model 1”, “Model 2”, … is repeated unnecessarily. An improved plot would have the outputs for each model paired together and use a different colourmap to distinguish Quantity one and Quantity two.
Brushing Up Science 
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