iTunes say that the video that I try to synchronize into my iPod is not playable in it. Anyone know what's wrong?

What format are the videos? They'll need to be mpeg4 or H.264 for the iPod. So, if the videos are in another format, you'll need to use a converter.

I'm using Windows XP & I use 3GP_Converter (free). Videora's another free one that's popular. If you're using a Mac, someone recently said that iSquint converter worked well.

There's heaps of info & links to different converters in the thread below.
How to transfer music to my iPod (& iTunes)