http://androidforums.com/motorola-droid/92893-moto-droid-touchscreen-problem.html There are a bunch of reasons that can make this happen ranging from 3rd party chargers to humidity to static electricity charge you might be carrying to an application that doesn't play well with others. You're not the first person with this problem, and trust me, you won't be the last. So here are some troubleshooting questions:
Does this happen when the phone is hooked up to the charger?
Are you using the Motorola charger that came with the phone?
Has the screen gotten wet or damp (this can have an effect even if the moisture indicators don't register anything)?
I know this sounds odd, but does it happen in rooms with carpet, and if so, does grounding help? Touch something like a wall outlet and then try to use the phone.
Are you using a screen protector?
Have you recently downloaded a new app?
Run through the list. This is a pain, but it's sort of a process of elimination thing to figure out what's causing it. Sometimes, I think the phone is sentient and tired of waiting to take over the world, so it acts out.