What does it take?

How much moving around does it take to turn a carbonated beverage in a keg into a foamy mess when you try to serve it?

I'm guessing it doesn't take much movement/bumping because I just moved a keg of root beer out and set it on the floor to put a keg of beer in my kegerator. Now it is sputtering and shooting out foam. I opened it up to check if it is near empty, but there is probably about 2 gallons left still.

Did I shake it up just like a pop can and now its not stable? Is there anything I can do to help calm it down or do I just have to wait?

If it's under pressure, and remains at the same temperature, it shouldn't be a problem if you let it settle for a few minutes.
If it's warming up, then it will be a problem. What you've done is by allowing it to warm up, the pressure it had on it will no longer allow as much gas to remain dissolved as there was when it was cold. Thereby, shaking will disrupt the equilibrium and bring a lot out of solution quickly.
Keep it sealed and wait until it's cold again before you start serving any, and you should be fine.

It's entirely temperature related. As the temperature increases, the pressure will increase and cause more foaming. A pan of ice would help the most.

That would do it, but I didn't have it out of the kegerator for more than 10 minutes, so I doubt it warmed up too much. Plus, it has been in the kegerator for 2 days and is still foamy/sputtering when I try to pour a glass.

It looks like there is air (or maybe CO2) trapped in my line. I think that is causing the sputtering. When the root beer is coming out it starts foaming up in the line, maybe that is where the gas in the line is coming from? Or is it that the gas in the line is causing the foaming somehow?

Maybe it is over carbonated, but its at around 25PSI and 37-38 degrees, so I can't imagine it is over carbonated...

I would depressurize the rootbeer keg, remove the Out post, and check the O-ring under the Out dip tube flange. It sounds like CO2 may be taking a short cut into the Out path, and that usually fingers that O-ring...

Cheers!