After almost two years of waiting, Google Voice's iPhone app has been finally approved in the App Store. It looks much better than the HTML5 web app and you can enable push notifications for voicemail and text messages.
Google Voice for iPhone doesn't beat the Android app because it doesn't integrate with the standard phone app, doesn't synchronize the inbox and doesn't offer advanced options for notifications, but that's because iOS has many limitations.
Google says that the application requires iOS 3.1 or a more recent version of Apple's mobile operating system. Google Voice is still limited to the US, but you no longer need an invitation to use it. Hopefully, Google will add support for the VoIP service from Gmail in a future update.