Q: How do I sync my videos and movies to my ipod?

Did you select them to sync?

Also see:

iTunes: May be unable to transfer videos to iPhone, iPad, or iPod

iTunes: Frequently asked questions about viewing and syncing videos

Some iPods have different troubles. Try doing a total sync. Mark everything you want to sync, from music, to apps,(Any that you already have on the device will remain there with the data you have on it, whether you resync them again or not.) If you do a total, additionally mark the videos and movies you wish to sync. See how that works.