Max is testing a very good solution to make deleting personal messages an easy task, but that solution may not be available for quite some time. In the meantime, deleting a personal message is a time-consuming taske You have to "archive" a message from you personal page or from the message itself, and then you have to go to your archive and click on the "delete" link in the message or the archive list.
Here's a shortcut from Jeri, our Tech Goddess:

Well, it's not designed to work this way, but it does. If you just start clicking on "delete" and keep going down the list as fast as possible, you may get quite a few threads, if not all of them, before the page changes.

And one from Joe Offer:

Another way is to right-click on the delete link for each message, and choose open in new window. Keep working on the original list, and keep closing the new windows as they open.
I also use that "open in new window" trick from the Forum Menu. I keep one Forum Menu open for a while, and open the threads as new windows, closing that thread's window as I finish reading.