Do you prefer a video with the band straight up playing the song (example, Nine Inch Nails' "March of the Pigs"), the band playing while some scenes provide extra story (example, Alice In Chains "Stone"), or a video where the band has little to no involvement with and is completely it's own film (example, Linkin Park's "Lost in the Echo")
I always like to see the artist in the video, even if they don't perform. But, if there are to be both performance and "story" elements, they need to be combined as smoothly as possible for a cohesive result. That's what really matters to me, that different elements work well and, importantly, work well together, resulting in something which is greater than the sum of its parts. Anyway, I prefer vibes or moods to full-on plotlines. Even simple performance videos should provide moods.
I generally like what fits the song the most. Sometimes when I'm listening to music there are songs that have like an "evident" story to me, I picture it in my head and everything, so when they release the video and is artist-only or something along that I get really disappointed, because I felt like the song had a lot of potential. It happened to me with "Already Gone" from Kelly Clarkson and many other videos. I don't really like videos where the artist has no involvement whatsoever, when that happens I feel like the music is just a background track.
With both of your replies, I realized there are too many exceptions and such to be able to label what you like in a music video only by the three options I put... Well, I failed.
A) is often uninteresting. B) is often the best option because it doesn't let the fans down while adding up to the lyrics/story, as you've said. Also, when the band themselves are involved, that can be great. C) is often disappointing to the fans, but is better than just the band performing because of the adding up to the lyrics/story again. Also, some songs have lyric videos as their official music videos, which I find lazy.
I like the ones which are fucked up, either in a weird way or a psychedelic way, or in a stupid and hilarous way, or which are so bad they become good. Those makes me feels something, they either amuse me or intriguate me. On the other side, I'm not really a fan of all those "modern" videos where a band/MC/singer/... is just showing his face and his way to move. And those with a story, but scenarised in a Hollywood-way, with all the cliché modern ways of filming something. Not my thing I guess