I've got hundreds of unread messages for years in my iPhone. They look like this:
And it would cost me long time and work to click on those messages one by one. Thanks to Google after searching online I found that Apple has introduced the feature to clean them once for good in iOS 8, which I didn't discover (link):
Beginning in iOS 8 you can mark all messages as read by launching the Messages app, tapping the Edit button and then selecting Read All.