App for international texting

If by "international texting" you mean being able to send SMS in local languages, have you tried to set up the correct keyboards in Preferences (General\International\Keyboards) then selecting the "world" icon (just to the right of the space bar) in the sms application.

I know http://www.FishText.com have one, but it's not in the App Store yet - should show up any day now, touch wood.

I've been using Yahoo! IM on Beejive and I can send SMS messages to Asia really easy and FREE. It works incoming and outgoing SMS to my app, not to mention it has push. Which country are you sending it to? You might wanna try Yahoo! IM to check it out, then purchase Beejive if your country is included.

tag

You can use the skype app. It's very cheap. You can check out their rates.

FishText is in the app store now. It's not exactly free, but it's the cheapest paid for service around at the moment. So if you wanted the reliability of the message being sent to South Korea i would take a look at it.