My number one fantasy fight growing up was Ginger vs. Mary Ann on Gilligan's Island. I usually pictured Mary Ann winning.
I also love Christina Applegate -- I would have loved to see her and her TV mom (Katey Sagal) have it out in miniskirts on Married With Children. Just imagine the leg action in that one!
Another youthful fave for me was Uhura vs. Yeoman Rand on Star Trek.
Another mother/daughter match would have been Marsha (Maureen McCormick) vs. her TV mom Florence Henderson on The Brady Bunch. Depending on the truth of various tell-all books, maybe they could have fought over who'd sleep with Greg.
The only Dallas beauty I really wanted to see in a catfight was little Charlene Tilton against some taller woman.
I also always had a thing for Mrs. C (Marion Ross) on Happy Days. I remember an episode where she came out as a harem dancer to spice up her marriage. I just about lost my mind when I saw that.
Sticking with the mature women, though this might sound weird, on The Beverly Hillbillies I always found myself attracted to Mrs. Drysdale (Harriet MacGibbon). I used to imagine cross-show lingerie matches between her and Tina Louise (Ginger on Gilligan's Island). There was always a lot of boob grinding and leg locking in these fantasies, and even though Tina was much taller, the fights were always a pick-'em event. Mrs. Drysdale actually did win a catfight against another granny-aged woman on the show.