It'll only took 16 months, but it's finally here. Google Voice is now available for iPhone and you can download it from the iTunes App Store right now. The app allows you to make and receive calls from your Google Voice number (using your iPhone's calling app as a proxy), send and receive free text messages, access your iPhone's address book, and read/listen to your voicemails.
Although they're often the Damn You Autocorrect!, Google Voice's voicemail transcriptions are still handy and especially useful when you have access to the voicemail as well. Google Voice for iPhone provides an easy-access inbox so you check your most recent voicemails like they were text messages. Incidentally, your inbox is where you'll also find recent text messages. You can reply via text or by calling to either.
Google Voice can't overtake your iPhone's phone app like it can on Android, but you can simply replace your iPhone's phone app with Google Voice for basically the same functionality. When you make a call through Google Voice, Google's backend routes the call so it'll come from your Google Voice number. To make the call, it commandeers your iPhone's calling app and returns you back to Google Voice when you're finished. When a call comes in on your Google Voice number, it'll be forwarded to your phone in the same way it's always worked.
Text messages work just like you'd expect. Google Voice sends texts that appear just like any other text message, and when you receive a text message sent to your Google Voice number it shows up as a push notification on your iPhone.

While much of this functionality was available in Google's HTML5 version of the app, the native app is particularly great because you have direct access to your iPhone's address book, better calling integration, and better text message support. Google Voice is available right now, completely free, so go get it!