Algorithms that would benefit from variable transformations?
It's not necessary for all features, but most algorithms would benefit from making highly-skewed or heavy-tailed features more Gaussian-like.
Transforming to Gaussian makes the data symmetric and removes both heavy and long tails. That does a similar job of normalizing to $[0,1]$, without aggressively smashing the data into a bounded interval.


Side note: Transforming to standard Gaussian means that the center scale of every feature is the same. This is very helpful in making sure that your model learns "fairly", rather than putting undue influence on the feature with greater variance. See here for an example of how un-standardized data can harm K-means results. See also the comments in the other answer about regularization.