I'm trying to swipe a couple photostream pictures onto a borrowed windows laptop, but I can't find any way to do that via the web.
Can I access my photostream in any way other than iTunes? I'd rather not install it on someone else's PC.
On a Windows system you can access Photo Stream by installing iCloud Control Panel for Windows.
Based on the description it allows you to access all the features within iCloud. Though this is only supported in Vista and Windows 7.
The most native way to access your Photostream is indeed installing the iCloud Control Panel, just like Justwes told you to do.
If you are looking for some web-based solution, you should try the freshly updated Dropbox app. It has a feature called Photo Upload, which will enable you to automatically upload (all) your photos from your iPhone to Dropbox. By doing so, you will not only earn up to 3GB of extra (free) space, but you'll also be able to access your photos by surfing to your Dropbox account!