Are you asking how to save an image or video you get via SMS, or MMS? You can long-press on it and then take action.
If you are asking if you can save your messages themselves, I think an app like MyPhoneExplorer might work for you. You load the app from the Market onto your phone, and download the identically named application from the web onto your PC. I believe it had the ability to backup your messages on the PC.
I can see where that would be a convenient option papasha3! My best recommendation would be to forward the messages to an e-mail address. Once the messages have been forwarded, the capability to edit them and save them will be dependent on the specific e-mail client. I trust this information was hlepful.
Sincerely,
JonathanK_VZW
VZW Support
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