Members of the rooted crowded running an LG G2 on Verizon can go grab the first nightly builds available of CyanogenMod 10.2. For those unfamiliar, CM 10.2 will bring a vanilla Android-like experience to your device, complete with a ton of customization options and tweaks to make sure you are getting the most out of your device. CM is basically the industry standard of custom ROMs for Android.
Again, you will need to be rooted and running a custom recovery on your G2 device. If you have that done, flashing the zip file should be relatively easy for any seasoned flasher. You can download the ROM by following the via link below.