My iphone takes photos, automatically uploads them to the cloud in a cool way and then they arrive on my iPhoto without me having to do anything - that's excellent but is it also possible for me to view the photos online through a browser or similar? Apologies if this is a particularly easy question - my google-fu is failing me today...
Modern Answer (2016): This is a feature of iCloud Photo Library, that launched in 2015 (and was in beta in 2014). With the updates to Photo Stream/iCloud Photo Library, your photo library is now viewable on iCloud.com.
Original Answer (2012):
This feature is called Photo Stream, and at this point, there is no web version of it.
The previous iteration of iCloud, which was called Mobile Me, did have a gallery option, but did not have the direct upload integration like Photo Stream (you had to manually post images).
iPhoto for iOS (but so far not Mac) can create galleries (called Journals) on iCloud which you can then share. Although you have to do this manually, and it doesn't operate on the photo stream automatically so this doesn't do exactly what you're asking about. But I mention it because you might find it helpful.