I gather that the rest of the hockey world barely acknowledges our existence again, now that the new team shine has worn off. Aside from Byfuglien or the drama train that was Evadnder Kane, no one really talks about us in major sports outlets much.
We've begun to develop rivalries with our Central division brethren the past few years however. St. Louis in particular, last season. Of course, when we ended up playing 4 or 5 times in one month, tempers tend to flare. I know some Avs fans don't care for us either for some reason. Minnesota is a good one, especially since of our geographic location to each other. Lots of Jets fans go down there to see the team. Maybe Arizona due to our ties with the old franchise? I mustn't forget Chicago though. The games against them have become much more impressive over the past few years as opposed to the routs that they used to put us through. I'd love for a full on playoff series with them. Win or lose, It'd be a war and entertainment at it's finest.
For me, personally, I still resent the Oilers for the beatings that they gave our old team and even though they have been mediocre for a decade nearly, I will still never cheer for them (The exception being last spring when they beat the Kings to insure our entrance to the playoffs for the first time in ages.)
The other team that I despise with a passion, of course, are the Leafs. But I've never required an NHL team at all times to hate on them.
As the years go on, we'll develop some more intense rivalries, for sure.