The first school of thought adopts an artistic approach to special effects, seeking to heighten the emotions projected by onto the viewer or otherwise strengthen the impact of the video. When done well, this can be extremely effective. When done poorly, this can lead to heavy-handed or incomprehensible symbolism. Any video which requires liner notes to be rendered comprehensible has probably failed to communicate properly as a video.
Example of Meaningful Effects: trythil's "always"
The second school of thought can be briefly summarized as “let's have fun”. These are effects used for visual appeal, like color in the Wizard of Oz. These generally have no artistic merit other than that the editor had fun creating them and thinks they look pretty. This can lead to stunning technical achievements, such as compositing two hundred clips into a massive wall, or videos where the editor got so caught up in placing lens flares that the original concept has been lost entirely.
Example of Effects for Appearence: requiett's "Phantasmagoria"
Most effects are used for musical synch. When the audio doesn’t justify a hard cut, or a hard cut won’t do, an effect is frequently what fits the bill. Color shifts, freeze frames, inversions, crossfades, and more are commonly used for musical synch.
Example of Effects for Musical Synch: Jebadia's "FIRE!!"
Sometimes, what the editor wants to show doesn’t exist in the source. However, if they can find enough pieces to work with, and are willing to invest the time, compositing is a viable option. This is where a shot or scene is fabricated using pieces from an anime (or more than one). Cutting out characters and other bits of scenery is common, and the results can be extremely impressive.
Example of Compositing: You choose Sam,the rest's "Because I choose to"
Example of Compositing: Zarxrax's "RVG Project 2004 - Track 34 - Surfing on the Blocks"