I personally feel like the Celtics/Heat rivalry is overblown. They beat us to years in a row in teh playoffs. Big deal. I felt the Pistons/Celtics rivalry had more juice than that. I don't have some irrational hate of LeBron James. He's the best in the league.
It's not only because they beat us two years in a row. It's because of the mentality between these two teams - there is a competitiveness and hatred that goes deeper than that.
Firstly there is the Boston vs Lebron rivalry. For years while Lebron was in Cleveland he was trying to get to a title, and each time it was Boston who knocked him off the perch. For years it seemed like the one single idea in Lebron's head was "Beat Boston". To make matters worse we typically dislike Lebron because he every single whistle goes in his favour - simply being Lebron gives him the benefit of 90% of calls. That's not something that's actually his fault, but you can't help but be frustrated by it every time we play the Heat.
Secondly there is the Wade rivalry. Wade has been practicaly fueding with Rondo for years now - the two absolutely hate each other's guts. Aside from that there is the hatred Boston fans have towards Wade in general for his consistently dirty play, and he seems to always save the very best of his dirtiness for Boston.
Thirdly there is the fact that they have (twice running) knocked us out of the playoffs, even though we dominated them in the regular season both years. Again that's not their fault that they beat us (it's what they're supposed to do) but it's still frustrating to us because as Celtics fans we KNOW we are more than capable of beating them in a 7 game series...and that's annoying.
Next there is Jason Terry - last year Miami beat us in the ECF. The year before that they knocked us out in the semi's and then went on to face the Mavs, and Dallas knocked off that Miami team that was EXPECTED to win a title. Jason Terry hit so many clutch shots against Miami that series, so you KNOW they hate him.
Now as if there wasn't already enough reason for hate between the teams, one of our most fan-appreciated players left us and defected over to the very same team. They generally talk nice about him, but you KNOW half the guys on our team cannot stand Ray right now for moving over to the enemy - especially KG. As a group of guys that were previously like brothers, I can understand that, and it''s only going to add to the rivaly.
So hell yes there is a rivarly.
Look at LA right now and the rivaly is no longer what it used to be. Aside from Kobe, Pau and MWP there is nobody else really on that team who has a history against us. They are in a different conference so chances are we probably won't play them in the playoffs. Even during the regular season, we probably only play them once or twice. The only people in LA I really can't stand are MWP and Dwight Howard. I dislike them both with a passion. Kobe I actually don't hate that much because I respect his competitiveness and his desire to win, and IMHO he's nowhere near as dirty as Wade.