Even though the iPad has that HD feel, there are plenty of HD files it can't stomach -- the maximum resolution for videos to sync via iTunes is 720p, and anything higher (1080i or 1080p) simply won't transfer. On the iPhone and iPod touch, the upper limit is even tighter; those devices can only handle 640x480 videos, meaning that a 720p file will stall out. Generally, movies or TV shows purchased from iTunes will arrive with versions tuned for both devices, but for anything you've created independently of the store, you may run into a spot of trouble.
There's an extensive walkthrough over at Gizmodo covering how to use Handbrake for downsampling your 1080i/p videos to a more manageable resolution, very helpful if you're in a DIY mood -- but there is an easier way. It takes advantage of a feature in an app you're already using: iTunes.
Just select your movie file(s) and check under the Advanced menu. See those two "Create..." options? The iPod or iPhone version will deliver a resampled video at a resolution the smaller devices can manage; the iPad/Apple TV choice will spit out a 720p file. All you need to do is select your choice and wait for a while... depending on the length of your video and the speed of your Mac, it may take quite a long time, but be patient. You can try out the steps with an Apple-provided sample file, if you like.
Once the conversion is done, you'll see a second instance of the video in your media list -- then you can sync at will. Note that if the file you're choosing is already adequately low-res, you'll see the dialog box below.