Data pre-processing is often a very important (if not the most important) step in a machine learning algorithm. Decisions trees are often an exception that they can work well without any pre-processing. But they may work better if you can identify some processes that might improve the quality of the decision detection.
As an example of other machine learning models: Linear Discriminant Analysis, or Quadratic Discriminant Analysis are both models that are explicitly calculated from the assumption of the distribution being a multivariate normal.
However, all that these models do is create either a 'linear' decision boundary or a 'quadratic' decision boundary to separate classes (in a classification problem)
This has been shown to give good results often when the data is not necessarily normally distributed; so my point being that just because a model assumes one thing that isn't necessarily true does not mean it won't still be a valid and effective way of generating accurate results.
Of course it might also fail miserably - herein lies the art of machine learning.