The i Phone has a few video chatting options, but Skype tends to be the best thanks to its ability to work on virtually any connection to the internet, good picture quality, and ability to communicate with practically every other platform you can imagine. I managed to hold a video call for 10 miles in a car (someone else was driving) on AT&T's network, which would be impressive even for a standard voice call considering their reputation.
Skype for i Phone is very simple, which is something the desktop app might want to consider. While Skype definitely does a better job with voice calls, its i Phone video chat works well and provides a good experience.
You choose the person you want to video chat with, press the video icon, and the call begins. It also lets you connect with practically any platform, making it possible to video chat with virtually anybody regardless of your location. Sometimes your video won't show up on the first try and you'll have to toggle between video and voice to get it to work. Usually everything works fine, but it's not a perfect experience.
The primary thing it's really missing (and will never have) is the ability to video chat with other services, but hopefully we'll get that from Fring (see the competition section) in the future.
Facetime is the obvious competition for Skype, as it's Apple's built-in option.
The problem is that it only works with other i OS and Mac users, plus it only works over Wi-Fi.
While we found the video quality was sometimes marginally better with Facetime, it was nothing to write home about.
That said, Facetime is either part of your device or it isn't.
Since there's nothing to install and you can use it as you please, it makes for a good alternative when needed.
Just don't expect it to be a good full-time option (unless all your friends and family members only have newer i Phones and Macs).
Fring (Free) is actually a very good alternative to Skype.
The video quality it provides is adaptive, meaning it'll shift upwards or downwards depending on what your connection can handle. It's also provides plenty of other ways to communicate, like voice-only and text, with several services instead of just one.