Making a music video is a different task from making a typical movie. All of the soundtrack is there already, and your task is to add a visual element to that soundtrack. From time to time, there is a video telling a story that has something additional at the beginning, or the end, or slightly edits the song in order to fit the video a little better. But it's not like shooting a screenplay where the closest thing to what's set in stone is the dialogue and a description of what's in the scene.
So, what is the best way to add a visual element to a song? I think that the most common thing is to show off the artist, and make something that just looks totally awesome. Buttrock and hip hop typically are the ones who do this most often. Put Your Hands Where My Eyes Can See might be one such example–visually stimulating, but I would be hard pressed to tell you how it relates to the song. AC/DC seemed to have nothing but videos showing them playing their instruments on a stage.
Possibly the least interesting kind of music video is one that is a shot for shot representation of what is going on in the song. I love Weird Al, but he is probably guilty of doing this more often than anyone else. When you hear the various lines of White and Nerdy, you can imagine quite a lot of what is going on, and in most places the video doesn't add very much to that. Or it does it in a way that was better in your head. (The few places where it parodies rap videos are somewhat clever, to give him credit where it is due.)
If one is looking to make a video that is a work of art, the ideal is to create a movie that tells a story that is very much like whatever story or narrative is in the song. Take On Me is the best example I can think of for this: it is a song about a man chasing after a woman, and so is the music video, but there is no direct correlation between any parts of the song and any parts of the video.
At first blush, this sounds like a dumb way to make a music video, but it allows for greater creative expression. The song and the video can have a kind of dialogue, where the video tells you something you might not have known about the song, and the song informs how one is to interpret the video. This is why I think Tool makes better music videos than just about anyone out there: they have figured out the full potential for what a music video can be, and they try to take it to that full potential. Sober is an elaborate metaphor about addiction (sometimes descending from the metaphorical into the literal), and so the video creates visual metaphors for addiction, going so far as to have a demon in it (or, at any rate, something that appears to be a demon). Both are meant to be super creepy, and having the two work together amplifies whatever creepiness they might have on their own.
Artistically speaking, to me, this is the greatest thing a music video can aspire to: accomplishing synergy with the original song, such that both the song and video are expressing things that they might not have been able to otherwise, or such that they are expressing what they were before at greater amplitude. When anyone talks about what they think are the best music videos ever, they will either have this quality, or simply look totally awesome--and looking totally awesome is also a noble thing to aspire to.