Yes you can, though it's a relatively new feature so you'll need your devices updated to the latest version of iOS or, in the case of your Mac, Mac OS X to ensure it's available.

It's a smart addition because when I first read about photo stream I thought "that'd be great" but then looked at all the banal and throw-away pictures I take with my iPhone (I use the photo album as a sort of visual notebook to remember books I want to read, where I've parked in a large parking lot, funny quotes or artwork, and even just random images that strike my fancy). Nothing bad or inappropriate, but having them automatically migrate across all my devices seemed a waste. Further, I wasn't clear whether there was any public access to the images that I was autosharing, though I now can see that they are indeed hidden from view unless I manually reshare them on a service like Facebook or Google Plus.

Indeed, it's Google Plus that got me to give photostream another try: Google Plus automatically uploads a copy of all photos I take on my iPhone to my G+ account. It's private and no-one else can see them, but it's incredibly convenient to take a photo and then have it magically migrate up to the social service.

Therefore why not do the same on my Mac? So I've turned photostream on and am using the below to delete specific images that I don't want to show up everywhere, though truth be told mostly I just ignore it. :-)

Let's start on the iPad, though, because that's where I commonly view and share photos. I'm in the Photos app and want to delete the first image, of "Paleo Pals":

To delete a specific image from Photo Stream, I'll tap on it to zoom in:

Look closely on the top right and you'll see five buttons: "Edit", "Slideshow", a button that has a box with an arrow pointing outward (for sharing the image), a box with a triangle below it (for using Airplay if you have a compatible device) and the trashcan icon.

It's the trashcan / delete button we want, so tap on it...

The screenshot is a bit small, but it says "This photo will be removed from the Photo Stream on all your devices." That's what we want, so tap on "Delete Photo", and...

It's gone from the Photo Stream and after just a minute or two it'll also have vanished from any other devices that are hooked in to your iCloud account.

On the Mac, you can find a similar function in iPhoto or Aperture. I use the latter, and in that case, when I'm looking at a photo in Photo Stream in Aperture, I can cmd-click to bring up the contextual menu and there's my option, right at the top:

That's all there is to it. Whether you're on your iPhone, iPad or Mac system, it's now easy to delete the shared images in Photo Stream that you don't want on all your devices. Magic. And useful too.