[blueskin_]

This is true for most default cursors, but custom cursor file formats let you change the coordinates of the active pixel (see: 'left-handed' mirrored arrow cursors, or crosshair-type ones.). The link 'finger' cursor on most OSes is a default example where the active pixel isn't the top-left one.

[Zecc]

For resize arrows it's pretty much a must.

[Sharlin]

The caret cursor over textfields as well.