Hyperspherical nature of K-means and similar clustering methods
K-means tends to create compact clusters, which means that geometrically, the distance between every two points is small.

K-means can create clusters which are ball-like if you use $L_2$ norm, pyramid if you use $L_1$ and hypercubes if $L_\infty$ is used.

As opposed to that there are clustering algorithms which first project the data into lower dimension (such as spectral clustering), which means not all of the points in a cluster has to be close, but rather "connected" via other points in the original space, which will make them close after the projection.

This allow you to find very nice looking clusters, such as this and that.