What do you mean by "moving side to side"?
Does the whole screen physicaly move sideway? (belong to the monitor section) Or is it the image on the screen that shift lateraly? (may belong to the Software|Operating system section)
Also, what is the brand and model of your monitor?
PC or Mac?
What operating system and version?
What is the brand and model of your video card?
If the monitor moves, it's base may be broken.
If the image moves, it may be a faulty video cable, a bad monitor, a dying video card or something else...
Electro, February 2013