Adobe's BrowserLab does this (https://browserlab.adobe.com/) for mainstream Mac/Windows browsers. You need an AdobeID (registration is free). I've found it much faster than browsershots.org (though you have fewer options). No mobile support, I'm hoping they add that soon.
Edit: 'no mobile support' = 'doesn't emulate mobile browsers'
Edit: 'no mobile support' = 'doesn't emulate mobile browsers'