It's been more than a year since I used the DVD mailing service of Netflix, but when I received the discs in the mail, there was no protection other than the sleeve over the disc which was inside an paper envelope. The entire package was only as sturdy as the disc itself.
But to answer your question, I would think a padded envelope would be more than enough to ship a DVD case. In the unlikely scenario where it gets broken, a DVD case is easily replaceable. If we are talking about some high dollar item where you want the original case, than I would recommend shipping it in a small box with enough padding around all sides to protect it. But really, I think that's overkill.
I think DVD cases are durable enough for the mail. Now Sega CD/Saturn jewel case long boxes on the other hand....................