Yea, Bayern - Madrid for me in Europe as well. As a kid it was the no1 European game. Madrid almost always seemed to come out on top, often being dominated by Bayern if I remember correctly.
Barca - Chelsea became an absolute classic since the mid 00's as well.
Barca - Chelsea is a good one. The record is 6 W, 6 D, 6 L. Some absolute classics and controversial ones in there.
Barca - United is another good rivalry. I think 14 matches, and we lead 7 W 4 D 3 L. 2 CL finals which is a rarity among big clubs.
Barca - Milan was a good one too until they fell apart in 2012.
As for Bayern - RM, the H2H was heavily in Bayern's favor until this decade. Bayern had 5 more wins than them and honestly they sort of spooked RM fans. "La Bestia Negra", moniker, for example. RM have punished them recently though and both have 12 W now.
Juve - RM is the 2nd most contested European fixture. Another really close one that RM leads by 11 W to 9 W for Juve.