The term “burned-in” is also known variously as “window dub”, “window burn” and “visual” timecode.
You can use the timecode effect in Premiere Pro 2.0 and later. Go to the Effects tab to the left of the sequence and expand the Video Effects folder. At the botton of the list is the Video folder. The timecode effect is located here. You can learn about the various parameters by searching for "Timecode Effect" in the Help section.
You can use After Effects to accomplish this task.