In Andy Field's Discovering Statistics Using SPSS he states that all variables have to be transformed. 
<a href="https://i.sstatic.net/5h4Wk.jpg"><img src="https://i.sstatic.net/axM4i.jpg" title="source: imgur.com" /></a>

However in the publication: "Examining spatially varying relationships between land use and water quality using geographically weighted regression I: Model design and evaluation" they specifically state that only the non-normal variables were transformed.  
<a href="https://i.sstatic.net/YuYuZ.jpg"><img src="https://i.sstatic.net/zBk0z.jpg" title="source: imgur.com" /></a>

Is this analysis specific? For instance, in a comparison of means, comparing logs to raw data would obviously yield a significant difference, whereas when using something like regression to investigate the relationship between variables it becomes less important.

Edit:  Here is the full text page in the "Data Transformation" section:
<a href="https://i.sstatic.net/v2Tya.jpg"><img src="https://i.sstatic.net/DmF1x.jpg" title="source: imgur.com" /></a>

And here is the link to the paper:
http://www.sciencedirect.com/science/article/pii/S0048969708009121