You can only ever view the time, date and number, and only if you're the account owner or it's your number and you have account member status on my verizon that the owner verified is ok.
I have great news for you, laulee. You can not only view the details of your messages, but through a new app called Verizon Messages you can see content of new messages online too. You'll need to make sure to create your own mobile number's account on My Verizon though to see your content. To do that, just visit http://bit.ly/xB4iTc and register your mobile number. The account owner line can log into My Verizon to change your number's access to an account manager through the "View Profile" section. Once you have at least account manager access for the line you're looking for, you can select View Usage under Account Management and then View Messaging Details for the number you're looking to see the details on.
To see the content of your messages you'll need to download Verizon Messages http://bit.ly/RziRAY to your Incredible. Once it's downloaded, you'll be able to log in using your mobile number's My Verizon log in at www.vzw.com/vzmessages to see your conversations.
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I cannot seem to make this work. I have followed all the steps but cannot see any place to view other phone conversations on the Verizon Messages app ... only my own.