Copy messages from my old phone How can I transfer my SMS and MMS messages from my old phone to my new phone?

My old phone uses Android 2.1 and it seems that you currently need at least Android 2.2 to log in to a Google account. Therefore, I can't use any tools which require a Google account, such as Android Market/Google Play.
You can try SMS Backup &amp; Restore. Install it on both phones. Backup the messages from the old phone (preferably in xml format). Transfer the file on the new phone, then use the app to restore the messages.

You can also try the method described in this answer.

Disclaimer: I am not related to the app's developer(s), just used it a few times.

Note: I am not sure if it still supports Android 2.1 or not.