Editors' note: This review has been updated to reflect improvements and fixes in the version released October 7, 2013.
Skype for iPhone lets you send texts and make both voice and video calls, and has a nice-looking interface. Unfortunately, it's missing a key feature, and I found that a bug makes the app unusable under certain circumstances.
Updated for iOS 7, the most recent version of Skype looks great, with a home screen that lets you view your contacts and gives you buttons across the bottom of the interface for navigation. Interface elements have all been simplified to fit in with the iOS 7 aesthetic and they are just as easy to navigate as before. You can add contacts through the Skype directory, save a phone number directly, or import numbers from your iPhone contact list. Besides contacts, you also have buttons across the bottom for Messages (IMs); a dial pad for calling phones; and a My Info button where you can add a photo, check your Skype credit status, listen to voice messages, and turn on call forwarding.
One of the greatest things about Skype is that you can make video or regular calls to other Skype users. As long as you have a connection and your friend has the Skype app on mobile or desktop, you can make free video or regular calls to him anywhere in the world. You'll only run into trouble if you want to call landlines or friends with mobile phones who do not use Skype. Obviously the best solution is for your friends to download the app, but if that's not possible on their devices, you can sign up for a subscription or purchase Skype Credit. The subscription prices are very reasonable at the time of this writing (here is the pricing page), with unlimited calls to landlines and mobile phones in the US and Canada for only $2.99 per month. To get the same deal to anywhere in the world, it costs $13.99 per month.