Some of our very own members on ThriveForums.org have been able to root the Toshiba Thrive Android Tablet. These amazing and brave hackers are making it possible for us to fully utilize the excellent Toshiba Thrive tablet, in any way we choose. Kudos to their ingenuity and hard work! According to their newest update,
UPDATE---

It appears that we aren't FULLY rooted yet, we still can't r/w the system directory, but we at least have superuser permissions to do almost everything else, and a fix is being worked on to make it fully r/w.

Currently ClockworkMod Recovery is only temporary, although a fix is being worked on to make it permanent. It appears Toshiba reflashes its own recovery every time it boots.

UPDATE2---
There is another boot image that can be flashed which will allow the system partition to be r/w, we'll host that soon

there is a method to remove the Recovery-reflashing method, post can be found later in this thread.
Here's a link to the thread so that you can read all about the amazing folks that helped with this project, and also learn about and potentially give it a try. Please be forewarned, you have the potential to "brick" your device if you muck up during the process or fail to follow the instructions carefully. But, if you are undaunted, make sure to let us know how it went, and how you are enjoying it. And, please don't forget to give a shout of thanks out to Bilgediver and everyone who was involved in the project. You can find everything at the source link below.

Source: ThriveForums.org and "Full Working Rooted Thrive Now" Thread on ThriveForums.org