I never really got too much into hockey (or sports in general) until around 07-08, after high school. I remember watching the cup run in 06 (my grad year - I remember grad was on one of the game nights they won) and it was devastating (the seeds had been planted by then). That being said, I didn't really adopt the Oilers first.
As one might gather from my user name, the Hawks are my other team, and they were actually my first team I got really passionate about (in the 07-08 year), mostly because I was a big fan of Toews and Keith. (Kane cemented my excitement for the team.) I've followed them primarily and their cup successes have definitely dulled the pain of being an Oilers fan. (I really didn't even expect one back when I first followed them, but certainly hoped for it and thought they might have something magical, which is clear now.) Last year was when the split became more 60-40 or 70-30 for the Oilers (was really rooting for Drai).
I guess I'm a hockey fan first, but those are the only two teams I really like. I'd consider bandwagoning the Sens (but I hate all the other Canadian teams). I also don't mind the Sharks.
Edit: I've never been sane.