[Doomimus]

Seems we've run into this issue more so in the second AMV Minis episode. Keep in mind that while lip-sync in anime is generally rather simple and stylized to begin with (as you can see here: http://www.youtube.com/watch?v=69A3aL3Yrs0), you should at least take the time to match the overall speed and duration of the mouth movements to the dialogue of the clip you're using. The more articulate and complex the dialogue is, the more you'll want to sync the movements to each individual syllable. This will be more obvious when the character speaks slowly as well.

In addition to the Evangelion/Futurama clip, here are a couple of great examples of lip-sync:
http://www.youtube.com/watch?v=rBwplkFt5nE&feature=channel_page
http://www.youtube.com/watch?v=kmmARL_595k&feature=related

The mouth movements from the Pokemon/Boat clip and the end of the Berserk/Waterboy clip aren't as intricately synced to the audio, but as long as they get the point across and aren't distracting, they can be just as effective.

Here's an impressive example using different mouth shapes (called "phonemes" in the animation biz), a rather rare find in anime. The character is behaving quite erratically on top of that.
http://www.youtube.com/watch?v=Pamy-gh0RlQ

Feel free to share your thoughts on lip-sync.

[Hockey-kun]

I try to use lipsync as little as possible since... I suck so bad at it lol.

I like using songs better. But when I do run into lipsync, I do try to make it near perfect.

[Filleraol]

I think it's fine, if there isn't too much of it and if the clip-maker put a decent amount of effort into it.
Too much of it (or bad lip-sync :P) makes me focus too much on it instead of the whole clip though