Tough one. Between Boston and Chicago, every other team doesn't come close for me. Calgary I don't despise, but really enjoy it when they lose for some reason and are my favorite team to make fun of, but there's no real ill will there.
Boston and Chicago i probably hate equally. Hawks one has more history, and add that Duncan Keith hit from last year and that probably puts them over the top, and against the Bruins no less, so that is really saying something.
I remember hating the Hawks way back in the day when they had Chelios and Roenick and I was cheering for Pittsburgh during their two first cup runs and I even hated them then, so it's funny how that works out and the cycle has come full circle with this generation of the NHL.
On the other hand, that Boston series was one of the most painful, infuriating things i've ever witnessed as a Nucks fan. Milbury with his big ****ing mouth, Marchand and numerous other things about the organization I can't stand. The Kings are a rival, but other than Doughty I still feel pretty neutral about them on balance.
Every other team in the League i have no issues whatsoever with. Except maybe Columbus just because they're so terrible. No jk, i love you Blue Jackets.