Remove vertical dotted indentation lines in Visual Studio 2017

Just press ctrl+E,S and it will be removed.

There is an option under Tools → Options → Text Editor called Show structure guide lines that should remove that.

The same thing in VS2019 is called Show guides for declaration level constructs in the section of Tools → Options → Block Structure Guides; you might want to uncheck Show guides for code level constructs as well.

In the last version of Visual Studio Code, downloaded in July/2017 (please note that this is not Visual Studio, but as @tambre pointed out, this may help in VS too), the name of this setting changed:

Go to the menu Code->Preference->Settings and search for "renderIndentGuides". The complete setting should appear as:

  "editor.renderIndentGuides": true,

Change it to false and that's it.