How to remap ctrl+arrow keys to move word to word for mac

You can change the keyboard shortcuts for changing spaces from System Preferences:

Then create ~/Library/KeyBindings/ and save a property list like this as DefaultKeyBinding.dict:

{
  "^\UF702" = moveWordLeft:;
  "^\UF703" = moveWordRight:;
  "^$\UF702" = moveWordLeftAndModifySelection:;
  "^$\UF703" = moveWordRightAndModifySelection:;
}

You have to quit and reopen applications to apply changes to DefaultKeyBinding.dict.

See http://www.hcs.harvard.edu/~jrus/site/cocoa-text.html or http://lri.me/keybindings.html for more information.