How can I change a command and cursor key bindings globally? I want to assign "Go to previous word" command to cmd← and "Go to beginning of the line" command to alt←.

In short, I want to switch the actions of cmd← and alt←. Similarly for cmd→ and alt→ as well. How can I accomplish this?
To swap the key bindings download, install and start Karabiner.

Open the menulet Karabiner -> Preferences... in the menubar, search for arrow and enable the swapping of the two command like in the example below (FYI KeyRemap4MacBook shown in the screenshot is the predecessor of Karabiner):