In iTunes you have videos in your music library, for example music videos you buy and download from the iTunes store and then show up under the artist in your music library, and you also have videos you import manually, under the "Movies" heading. If you import a video, for example your custom-made music videos, they will appear under the "Movies" section, not your music library.
You can add videos to a playlist and synchronise the videos and playlist to the iPhone, but unfortunately not videos which appear under Movies. So the only ones which will work are ones which are part of your music library. I don't know of any way to make videos appear in your music library except to buy them from the iTunes store.
[EDIT]
Correction - you can do it. Import the file in to iTunes. Go to to the Movies section and find the file. Right click it and select "Get Info". Go to the "Video" tab and change the Video Kind from Movie to Music Video. If you want you can go to the Info tab and change the artist name so it shows up under that artist. Or you could change the album name to "Music Videos" to group them together. Press OK. Then go to your music library and find the video(s). Drag them in to a playlist. Sync the iPhone and you can play them all from the playlist and it will automatically go to the next video once one finishes.
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moto