For those of us running iOS 5, we were thrilled to learn that the new messages app on the phone would send messages at data and not count against your sms tex messaging plan (as long as both users were on iOS).
Apple also touted syncing of these messages between iOS devices, however, many users have had trouble making this work. The trick to making this work properly is to use the same email address (probably the one you use as your appleID) on all the devices you whish to syncronize.
Here is your quick fix...
Go to Settings on your iOS device.
Choose the Recieve At
Choose Caller ID
Verify a matching email address
Note: Make sure the "check mark" is by the email address rather than the phone number (on iPhone)
That should do it. Also note, Apple will replace iChat on the Mac desktop with Messages when Mountain Lion is released this summer, but you can try that out in Beta here if you want to get a jump start. I mention that as this trick should also then work to sync messages to your desktop! I have been using it for a while now, and yes, this means you can "text" message your iOS friends from your desktop mac.