Raw Data:
Indeed it is (or was) quite common for aircraft such as the DC-9/MD-80 to power backwards off the stand on at least a lot of American airfields. I particularly remember watching this going on while I was refuelling (I think it was at Raleigh/Durham).
On modern airfields the ramp should always have an up-slope as you approach the gate (have you ever noticed how you might have to put a bit of extra power on at the last minute)?
This makes it easy for the tug to push you back even if you are very heavy. Therefore it is easy to get an aeroplane to move backwards if you should decide to dispense with the expense and inconvenience of using a tug and your aeroplane has a suitable power/weight ratio.
Having done a lot of reversing when I had propellers, I have to tell you that the secret is in knowing when and how much brake to use in order to stop rearward movement. If you get it wrong the aircraft will sit on its arse and you will suffer huge personal embarrassment.
If you are not as skilled in this manoeuvre as those who do it every day, please don't try it!