Before you get too excited, I must warn you that the process isn't for the faint of heart (you'll have to physically crack open the Revue's box and solder some wires in), and you'll need a brand new device that hasn't received any firmware updates.
That said, there will undoubtedly be those of you eager to give it a shot, so if your device qualifies, go ahead - instructions lie below.
In order to complete the root you will need an un-updated box, it seems as if the first or second update to the box closed the serial access hole. If you have a "virgin" box then you are ready to proceed.
1.) Open your box, there are 4 screws (1 under each of the soft legs on the bottom of the box), the rest of the box un-clips very easily. A better explanation is available at http://www.ifixit.com/Teardown/Logitech-Revue-Teardown/3788/1
2.) After opening your box you will need to remove the led bar and look at the top front of the board. Locate the pins labeled UART1. These are the pins you will be sodering to.
3.) Solder 4 wires to your board. The appropriate pins can be view here:http://gtvhacker.com/index.php/File:XJHay.jpg . You MAY only need to solder to TX, RX, and GND.
4.) Attach wires to appropriate pins on your USB->TTL device
5.) Connect to the USB->TTL device on your computer using a program like Minicom or Putty. The appropriate settings are speed is 9600 baud with 8n1, make sure flow control is set to none.
6.) Reboot Revue into recovery mode by holding the pair button on the back of the board until the box shuts down and comes back up. Then press Alt+L until "FORMATING DATA:" shows and stays, a menu should appear shortly after system is done clearing partitions. (More info: Logitech_Revue_Technical)
7.) If setup is correct so far you should be seeing logcat output through your terminal program (Putty/Minicom). Shortly after you will be presented with a # sign which is your console.
8.) Proceed to software portion.
1.) Place all files in manual update on USB (preferably to ext3) device keeping all the files inside of the "updatec99" folder for easiest installation.
2.) Insert the USB and run the following command for an ext3 USB device "mount -rw -t ext3 /dev/sdb1 /sdcard" substitute ext3 for vfat for a fat32 device (Also remove quotes)
3.) In minicom/putty browse to the /sdcard directory with "cd /sdcard/updatec99".
4.) Execute the update with the following command "sh manual-update.sh"
5.) If the process ends prompting "Complete" you are finished and may restart. You will then have adbd running on your Revue and can connect using "./adb connect LogitechRevue". If the process does not prompt you with "Complete" but some other error you will need to make sure you do not reboot your Revue or it may be bricked.
You are now complete and free to install applications on your box remotely through adb.
Note: when booting in normal mode, you will not see any console output. If you want a serial console again, go into recovery.
After rooting the device, you can (optionally) install the Android Market, as demonstrated in the video below:
Yeah, this isn't exactly the simplest root method out there, but if you own a Logitech Revue and are desperate for freedom from the networks/the ability to install Android apps, it's not like you have much of a choice.