In Edit Mode, in the 3D View, is there a hotkey for toggling between vertex/edge/face editing?
From Blender 2.8 on wards, there are the following hot keys while in Edit Mode:
1 for Vertex select
2 for Edge select
3 for Face select
You can add multiple active modes by holding Shift while pressing one of the 3 keys, allowing to activate all 3 at once if so desired.
Holding Ctrl on the other hand, when pressing 2 for example would limit the selection mode to the edge selection again, regardless which selection mode(s) was/were selected before.
Other then the direct hotkeys (not sure why the specific hotkeys are not shown), the information regarding the use of Shift and Ctrl can also be found by hovering over the icon for the selection modes.
This is based on the default installation of Blender 2.8+ addons can and have changed those hotkeys.
Should there be an issue with the default hotkeys, it's recommended to first go in the Blender Preferences and look under Keymap and search for 1.
In the Mesh section we find the Edit Mode related hotkeys:
marked red the important parts for in this case the vertex selection key-bind
@Xylvier's method works best if you have a numpad section on your keyboard.
However, as a corollary, for those who are 1) on laptop using the emulated numpad and 2) like single, but not mixed modes, you can just set the first three by pressing, say Ctrl-1, -2 or -3 for these (or Shift-1, etc) as he shows for the existing 1, 2, and 3.
Normally, for most software, as he points out, Ctrl is use for toggling a feature. Shift is for adding. But, for those of us who like single mode (vertex, edge or face - but not more than one mode) you simple use one of these prefixes for making this a unique keystroke.
The reason you use the prefix is so you don't mess with the views (you probably emulated 1 is for X, 3 for Y, etc). Also, you probably don't want to "fix" the ones farther down in the list if you don't like to have more than one edit mode selected - they work in the sense that the don't do anything, since you don't have a numpad. That is, the ones with the extended and expand check boxes are probably what you don't want - unless you really want to try using the mouse to do multiple modes.
Hopefully useful for those of us on Macbooks that like the old single mode method.