The first one was the best one, when Krystle tears Alexis's studio apart after an entire season of being bullied by Alexis and snapping when she finally realised that Alexis was responsible for causing her miscarriage. It was the highlight of the 1981-82 season.
The second one is probably the most famous, and in fact I saw it at the new permanent exhibit at ACMI the other day. It is of course the lily pond.
After that they seemed to have at least one fight a year, perhaps the most innovative being a mudslide rip-off of Romancing the Stone. Over the years the somewhat tacky value of girl-on-girl action was increasingly exploited by Dynasty as Alexis was forced to battle Dominique and Sable, and the younger girls like Sammy Jo and Fallon also got their share of catfights. To me, this all seemed to be a bit low-brow, whereas these first two catfights between Krystle and Alexis were so shocking and new - no one had really seen women behave like that on TV before.
One thing that is always amusing about the Krystle/Alexis catfights, and particularly obvious in the first clip here, is how little there is of Joan Collins - it is patently obvious that most of the "Alexis" we see is a stunt person in a wig. Famously, Joan Collins hated to do any of the 'physical' scenes and used a double for all but the most necessary shots, while Linda Evans apparently loved getting into the fights and did as much of her own stunt work as possible. The violence emanating from Krystle/Linda at the end of the first clip where she smashes Alexis's portrait of Blake is truly frightening. Although the two actresses spent years claiming to be friends in real life, Joan Collins recently dished the dirt in a rather tacky article in which she claimed that Linda physically abused her during a recent 'reunion' play the two women did. I guess some of that animosity, whatever was at the core of it, must have contributed to what made the on-screen hatred between Krystle and Alexis seem so realistic. And it sure made for some good catfights.