Update: 5/27/2022: They keep moving auto-merge. In Blender version 3.1.0 while in edit mode, the auto-merge has a convenient on-off toggle and link to the auto-merge settings in the upper right corner. These buttons are visible when the “Tool Settings” are enabled. To enable the “Tool Settings”, click the “Tool Settings” from the View drop-down menu until there is a check mark next to it.

When you move a vertex over another, many times you want the two to become one. There is a tedious way: Move the vertex and then merge. Or the easy way: Enable the  Auto-Merge option and then just move one vertex over another.

In Blender 2.80, the Auto-Merge option has moved. It is now in the Active Tool and Workspace panel under “Options”