UPDATE 12/28/2013 – Note: before resetting iCloud, sign out and sign back in. This is a quick fix for Photos not downloading to a computer with the iCloud app.
May 5/16/2012 – Icloud Photostream stopped working on my Dell desktop, Dell Laptop and my wife’s Toshiba laptop. It was still working on my Mac Air and iPad. To fix the issue with the PC’s I reset my Photostream. During this time the iCloud app on the three PC’s froze when trying to launch Photostream options.
iOS6 Log into the iCloud web page, click on your name, then click advanced. From here you can reset your Photostream. Pictures taken between 5/16 and 6/1 did not come through. My next picture taken on my iPhone did.
EDIT for iOS7 click your name and then click Account Settings. Then click Reset Documents and Data. I have not needed to do this.
It is possible an IOS update caused the issue. I am not that concerned why it failed. iCloud is new and I expect it be initially buggy. Photostream is the only iCloud service I use.