Jestin,
Usually that (but by no means always) means an addon is behaving badly or a config variable gone wonky. Even if it was fine on your old system, it might not be fine on your new one. Or an update could have changed things.
To test if that's problem, rename your Interface and WTF folders (which will temporarily pretty much make WoW run as if it's a clean install) and see if the problem continues. If it stops, then it's a tedious task of turning them on a few at a time and resetting up the settings and narrowing down which one is causing it. If it doesn't solve it, delete the new Interface and WTF that WoW will have created and rename the folders back to their original names and you'll have everything set back up the way it was.

If it's not an addon or a bad config setting, then it's probably something with your system. Unfortunately, tracking it down in that case is a lot more difficult. The easiest things are to make sure you have all the latest drivers and OS updates, if you have a DX11 video card enable DX11 by adding SET gxapi "d3d11" to your config.wtf file, if you use Win7 turn off automatic wallpaper changes in your theme and if you run WoW in a window try running it in fullscreen instead.

From there you might look for BIOS updates for your mobo, disable unnecessary windows services, run memtest86+ to check for faulty RAM, stress test your CPU and RAM with Prime95 to further check for hardware issues, run Furmark to stress your graphics card, turn off features such as Turbo Boost (the shifting can cause lag spikes if it's implemented poorly by your Mobo), there's tons of possibilities and if you aren't very technically savvy, you might end up causing even more problems than you fix (especially if you start digging around in the services or your BIOS, the testing should be fine as long as you keep an eye on things)