Making the Backspace key go to the previous folder in Finder

You can press CMD-[ (as shown in the "Go" menu). Using the regular way from there (Keyboard Preferences -> Keyboard Shortcuts and assign a new shortcut for the "Back" entry) doesn't work since the "Keyboard Shortcut" field does not accept the backspace character. But you can:

• Go to System Preferences, Keyboard, Keyboard shortcuts
• Create a new keyboard shortcut for Finder with the Menu Title "Back"
• Use any arbitrary keyboard shortcut

Then edit the file $HOME/Library/Preferences/com.apple.finder.plist and change the keyboard shortcut to "⌫" for example using XCode:

Now, if you restart Finder (using killall Finder or the Force Quit Applications dialog) you will be able to use the shortcut:

However, as pointed out in the comments, the backspace key is probably not usable in the keyboard dialog for a reason, since using it as a shortcut will trigger the action when you have the cursor in an edit box, where you'd want backspace to remove characters.

While the solution offered by barbaz is a decent one, there actually is a perfect one :), which removes the limitation that doesn't allow you to use Backspace in text fields in Finder (e.g. when renaming files, or typing in the search field).

1. Install an awesome Karabiner app that allows you to remap almost anything you don't like to anything you like
2. Find and edit private.xml file per instructions in the link (and read how to update Karabiner to include private.xml in the main list when you get to step 4)

3. Insert the following code and save private.xml file:

   <item> <name>Backspace in Finder moves Up</name>⌥ <appendix> (except when editing text fields)</appendix> <identifier>private.Backspace_MoveUp</identifier> <only>FINDER</only> <uielementrole_not>AXTextArea, AXTextField</uielementrole_not> <autogen>__KeyToKey__ KeyCode::DELETE, ModifierFlag::NONE, KeyCode::CURSOR_UP, VK_COMMAND</autogen> </item>

   This does the following:

   • Assigns ⌥ Opt + ↑ to Backspace key.
     • Note: in my OS X Yosemite it is the shortcut for 'Go Up' command in Finder (e.g. it always goes to the folder one level above the one you're in). If you don't like the 'Go Up' command and would like to go to the previous folder - define your own shortcut as per babraz' answer, then paste the respective key combination instead of CURSOR_UP, VK_COMMAND code above
   • Limits this command to Finder only
   • Limits this command to non-text fields only
4. Open Karabiner and click on "ReloadXML" button (see link in 2. for details on how to add custom private.xml)
5. Select "Backspace in Finder moves up" command
6. Enjoy :)