Videos can be deleted for a few different reasons...like they'll be broken (no longer viewable) or they'll be inappropriate. Also sometimes they're not deleted and just moved to a more appropriate spot.

As for ones that no longer work and are still in the spot...link sums up what to do in a situation like that :)

the videos arent actually uploaded to fanpop but just embedded. the sites which actually host the videos (like youtube, tudou,dailymotion) remove a video but the link to fanpop still exist. thats why you need to do what snerkie writes in her very well written article..report to fanpop that the original site removed the video.
make sure you ALWAYS click on the link first and read the description of the video..(sometimes its a preview etc)before reporting it- make sure its really broken

Yes, often a video will not work embedded, because the person who posted it on the video sharing site (YouTube, dailymotion, Guba, et cetera) has "disabled" embedding (which means that it will never play in another site like Fanpop). In such cases, the video will still work on the original site, just not on Fanpop. Such links are NOT broken and should not be reported as such. Playing video embedded is not a requirement for video links, even though it may be frustrating when they don't.