[AC Question]

I want to copy entire text message conversations to my computer so I can read them and save them on my hard drive.

[Matt247]

Download a pc suite software, you can also backup contact numbers to pc.

[Rukbat]

As SMS - SMS Backup & Restore. (SMS format is xml, so if you can read xml [it's not difficult, just ignore the tags], I'd save it that way, so if you lose what's on the phone, you can restore it.

As text - SMS to Text.

[doogald]

I use smsbackup+, a free app in the play store, to backup all conversations to a label on my gmail account. It's automatic, backing up within a few minutes of receiving a message (so you can delete something unimportant before it backs up) and every hour otherwise (though you can configure that to be more or less often) to back up what you've sent. I like it because I just done have to think about it - it just backs up. Then you should be able to use a standard mail app on your computer to copy conversations to your pc.