Backspace doesn't work in Visual Studio

In Visual Studio go to:

Tools 
Options
Environment
Keyboard

1. Find "Edit.DeleteBackwards" command.
2. In "Use new shortcut in:" dropdown select "Text Editor".
3. In "Press shortcut keys:" click backspace so it would show "Bkspce"
4. Click "OK".

Backspace should start working for you again.

I solved this issue resetting keyboard mapping scheme.

Tools -> Options -> Environment -> Keyboard -> Reset.

This seems to happen to me when I open a solution and there are files already open. I used to close the files, then close and re-open the solution to fix it, but now I just hit Alt + Enter.

Here is the blog where I found this trick.