539 votesmarkgoodson commented
Actually you can do this using Evernote. I just tried it and it worked really well. If you just select the message thread by clicking to the left of the first sms in the message window and holding as you drag down through the window/thread (it scrolls nicely). Then use the Evernote web clipper to "Save selection". I can see myself using this particularly for business messages where you might want to save a thread to a CRM system or into Evernote for future reference.