I can remember being obsessed with "The Matador" by a country artist named Sylvia when I was a little boy - even claimed it would make me better when I was sick. (I was always sick - had walking pneumonia for a looooong time before it was diagnosed and treated. Being able to get up and do anything that didn't involve video games, reading, or watching TV was basically a matter of tricking myself into pretending I felt up to it.)
I obsessed over getting a copy of the album "Rage" by the group T'Pau, even though I had never heard anything off of it. I had the album before, "Bridge of Spies", and the album after, "The Promise", and loved everything off of both - and I knew "Rage" existed because of an artist information book, but copies were not to be had in the United States. I even stayed up late one night to call a big record store in Germany that I had gotten the info for, trying to use a phrasebook until I found out the guy who answered the phone spoke English. Took me 6 years to get a copy - one of my locally owned record stores joined my search, and managed to get me one (from Japan, no less) after a 6 month delay on their order.
About a year later, eBay became a thing, and there's been several copies of "Rage" available constantly there ever since!
And most recently, I obsessed a bit over Marina and the Diamonds. I saw Marina perform "Primadonna Girl" on The Graham Norton Show and immediately felt that she had the same sort of potential to be huge that I had instinctively felt Gwen Stefani had back when I saw No Doubt's first appearance on Conan. Unfortunately, even though Marina is insanely talented, either the music industry just isn't what it used to be, Americans have lost all taste, or both. (The latter isn't totally fair, since Marina has caught on well with friends I've introduced her to. Americans just aren't exposed to the best music - the Brits get it all.

)
[yt]https://www.youtube.com/watch?v=Gj5L9SYhoSE[/yt]
I am obsessed with 80's music. I think I even once dialed 867-5309 and asked for Jenny.
When I lived near Springfield, MO, 867 was a valid local exchange, and people at the high school used to use to school payphone to call it fairly regularly and harass the older guy whose number it was about wanting to talk to Jenny, and he would get really upset. One day I called and explained why they were doing that to him, 'cause that's the sort of dweeb I am. That was right before we left the area, so I'm not sure what effect that had.