If they are bought/rented through the iTunes Store, they will not work due to the DRM that Apple wraps around them to prevent using them on non-Apple products. You can use a program called TuneBite to record the video into a new file that does not have the DRM, and then you can copy those files over to your Android device.
If the movies and shows you have are self-created (your own DVD rips for example) for iPod/iPhone use, they will play properly on your Android phone with the build-in Gallery player.
As long as the files you have do not exceed the resolution of your phone (Droid/X/2 has 854x480, most of the rest of the Android phones have 800x480) and are encoded at a quality of 1500Kbps (or lower for video) and 160Kbps (or less) for audio.
To view this information for your files, just play one in Quicktime, then in the top menu click on Window and then Movie Inspector.
Just to let you know, there is a dedicated video-section on these forums as well, so if you do have any additional questions, have a look there.
