The Reminders app is a great way to share a grocery list with housemates or your significant other. Set up sharing on OS X Mountain Lion or on iCloud.com by clicking the broadcast icon to the right of the list you wish to share. Once your recipient accepts, changes for that list will synchronize across everyone’s devices.
For some strange reason Apple has not given iOS devices the ability to set up sharing, though once it’s configured from your Mac or the web it works across all your iCloud-enabled devices.
Just be aware that any time someone else modifies the list you’ll receive an email. To stop them you’ll need to set up a filter in your email.