Viewing vertices in ArcGIS Desktop?

There is an example in the SDK samples http://resources.esri.com/help/9.3/arcgisdesktop/com/COM/ExtendAO/VertexLineSymbol.htm

Description This project provides a custom symbol to draw a line and its vertices. Simple custom functionality is provided to alter both the symbol used to draw the basic shape of the line, and the symbol used to draw its vertices. A property page is also provided to allow users to edit the properties of the symbol using the user interface.

I recommend that you vote for an ArcGIS Idea entitled Draw vertices:

It would be nice to display vertices at all time. Currently a line has to be selected for it to draw vertices. Maybe a button to turn it on and off.

You could use the free draw vertices tool from Ian Ko's geowizards. Works very nicely.