When directly editing a mesh, it’s useful to be able to rapidly switch between Vertex, Edge, and Face modes. If you’ve ever used 3ds max, these shortcuts are helpfully right next to each other. Here’s how to change modes in Blender:

Version 2.79

Ctrl+Tab brings up the selection list for the desired mode. Note that you must be in Edit Mode and have a mesh object selected for this to work, since it’s the same shortcut as Weight Paint in Object Mode, and enables Pose Mode when an Armature is selected.

Version 2.8

The new shortcut in 2.8 is ⇧ Shift+[1] for Vertex, ⇧ Shift+[2] for Edge, and ⇧ Shift+[3] for face selection. There are also three buttons at the bottom of the 3D Viewport pane that switch modes. Unlike 2.79, the selection modes in 2.8 actually allow multiple modes to be active simultaneously. In my experience, they work great for decreasing the amount of context switching, but sometimes more geometry is selected than initially intended.