There is a lot of information and some mis-information in this thread. Let me see if I can help.
AUTOMATIC.
With an automatic transmission, when the engine is running the torque converter spins and causes the transmission fluid (read OIL) to circulate to all the moving parts of the transmission (bands and clutches).
When towing, the spinning of the rear wheels will spin the clutches between the steels within the drums of the automatic transmission without the benefit of having the oil being circulated by the torque converter. This is a quick way to destroy the automatic transmission.
Removal of the driveshaft is essential. - Also - when removing the DS, you can subsequently remove the slip yoke from the front of the DS and secure it on the end of the output shaft of the transmission (wire ties). This will stop the transfluid from leaking out as you tow.
MANUAL.
A manual transmission consists of an output shaft, an input shaft and a cluster shaft. These shafts are holding the gears and sliders and are sitting in a bath of gear oil. As the transmission is turned, the oil is splashed throughout the casing and the moving parts are kept lubricated.
In a towing scenario (Neutral Please), the output shaft will be turning, but the cluster shaft and the input shaft will be stationary. The turing of the output shaft will keep the moving parts of the transmission lubricated by splashing around their oil bath just fine. There is no need to disconnect the driveshaft.
Having said all that, I much perfer using a car trailer rather then a tow dolly. Better control, Increased stability, and a small bit of insulation against damage should some jackass run into the rig while you are transporting your vehicle.