Staying away from the Japanese-language videos, since I'm sure those will be well-covered by other members. For now, I have these....
If you're more into effects videos, this may be a video to turn to. It combines a number of creative effects with the typical brutal imagery and angsty story that Elfen Lied is known for.
This video showcases the more serious side of Gravitation, by showing the tumultuous relationship between Yuki and Shuichi. It's also a nice overview of the series as a whole.
There are two main feelings that you'll get from this video's story. One, that it's a stalker story, a fairly common theme in projects involving Perfect Blue. Two, that it's the story of a girl being told through another person's eyes. Either way, this is well worth the watch.
A classic video that can be best summed up as an overview of the X OAV, which is, incidentally, an overview of the anime itself. Just a nice romp through some E Nomine music.
It's tough to describe this one. It has a fairly intricate story, but even without understanding that, it's a great video. Read the description if you're curious about what he was going for in here.
This is easily one of the best MEPs I've ever seen, both in terms of editing and the lovely and compelling song that was used. Seamless transitions between tracks wrap this all up into a neat package that flows like a video that has been edited by an individual. Get it and I promise you won't be disappointed.