In the 80s, some (OK, only a few) uses of monsters in videos were actually related to the song itself. Sometimes, the relationship was only as close as a cultural reference.
For example, let's take Walter Egan. He had really only had one hit: if the lyric "For you are a magnet/and I am steel" doesn't start ringing in the back of your brain, count yourself lucky.
(And don't look it up - just trust me, OK?)
Meanwhile, he had... well, a kind of non-hit, a song that basically went nowhere, but got a little (very little) airplay, mostly based on a video that also didn't go very far. It's alternately rendered, depending on where you look, "Fool" (or "Full") "Moon Fire." (And, really, nobody but Walter, his agent, and his wife really give a crap what the lyric is...)
In 1983, the Rolling Stones released Undercover their (yes) 23rd album (not counting anthologies and outtakes). And it included an unmemorable song called "Too Much Blood," where a leaden Mick Jagger tries to rap, using the details from a story about some Japanese man murdering a girl in Paris.
The whole limping, abused corpse of a song includes Texas Chainsaw Massacre references and the Sugar Hill Records' horn section, and Mick completely fails to engage the audience with a song that the Stones have never performed live and which appears on no compilation album. But it does have a weird horror-movie video to go along with it, and includes Keith Richards and Ron Wood playing lead and rhythm chainsaws. Which has to count for something.
And of course, there's always 1988's hit from INXS, "Devil Inside" (INXS's lead singer, Michael Hutchence, depressingly, apparently didn't die from autoerotic asphyxiation, as the urban legend tells us - he just hung himself... it's sad when you have to let a good story go, isn't it?)
Of course, in the end, the fact that the video might actually reflect the content of the song has never been a major draw, has it?
Update (10/29/10): The longer I left it lying there in the ditch, the more I knew I had to go back and fix that fourth (now fourth and fifth) paragraph, with the poorly-worded description of the Rolling Stone's song. A run-on sentence with pronoun mismatch and some unneccessary (and apparently completely random) words thrown into the mix could not be allowed to continue. So I put it out of its misery.