I'm mostly always auditioning songs for vids in the back of my mind, but only rarely do songs actually ping me as good vid songs, I guess is what I'd say. Occasionally I've been watching a movie and found myself thinking of the song I want to vid it to in the theater! And sometimes I'll have been listening to a song for years before it occurs to me that it makes a good match for a fandom (often a fandom that I'm not as long-familiar with).

It's pretty common to rip the audio from movie trailers and make AMVs to them, and I've done that. When I made my AMV that used the audio from a Bond trailer, I think what convinced me to combine the two was remembering one of the Bond villain's lines that was in the trailer and thinking that it described the anime, too. That was a fun AMV to make because most of it was just finding clips that had explosions in them to match the audio track. I've also seen some good vids lately that have worked native audio into the vid, which is something I kind of want to think about doing more.

I do also go from concept to song, usually by deciding that I want to make a vid for a fandom and then searching for music that works for it. Those vids tend to be more critical, I find, though that's not a very well-defined line for me.