If you would rather not deal with iPhoto (or Aperture) to get to the Photo Stream photos you’ve shared from your iPhone or iPad, CNET has a handy how-to for doing so.
In short: OS X automatically syncs your iCloud documents, which include your Photo Stream, to a relatively hidden location in your home user folder. CNET’s tip involves creating a Smart Search to make it easier for you to get to that folder to find your Photo Stream photos, but I cannot stress this enough:
do not alter the contents of your Photo Stream folder or any other iCloud-related folder.
This is a great tip for finding your Photo Stream photos for the purpose of copying them to other places or opening a new copy in an app and saving it elsewhere. But Apple designed iCloud so that you use apps, not the Finder, to handle much of the behind-the-scenes management process. Digging in through the Finder could very well cause trouble.