I don't know if this is significant, but Michelle Kwan is the only one whose birthday I know. And I think it's today! Happy birthday, Michelle.
There have been other skaters who have been far more accomplished but for sheer recognition, IMO Katarina wins.
Of course, it's my opinion and other people have theirs. I don't think we can ever have a definitive answer to this question.
Worldwide, I would tend to agree with Katerina Witt.
Definitely depends on generation. For me, growing up, it was all about Michelle Kwan. On the men's side, vaguely aware of Yagudin vs. Plushenko (and after a while, just Plushenko on his own).
A skater who should be world famous but isn't -- Carol Heiss. She was a five-time world champion (like Michelle Kwan) and Olympic gold and silver medalist (like Yuna Kim). First woman to do a double Axel. She could do a variety of spins and jumps in both directions.
Heiss had the bad luck to come along in between the skating movie era of Sonja Henie and the television era beginning with Peggy Fleming.
Actually, she did play the lead in a movie -- the not-quite-as-bad-as-it-sounds "Snow White and the Three Stooges.
I'd have to agree that Dorothy Hamill would be one of the best known skaters in the U.S., even today. Her bubbly personality, and of course that distinctive haircut, have made her very telegenic, so she's had more opportunities than many other skating champions. (Another asset is her very pleasing voice. She doesn't have that "little girl on helium" squeal that a lot of skaters and gymnasts have.) She was also the only ladies' gold medalist until Kristi in 1992, so for every Olympics between 1976 and 1992, she was invoked as the one to aspire to. I'd say that she, Michelle, and maybe Peggy Fleming would be the big names. Janet Lynn is revered among skating fans but these days probably isn't well remembered by anyone else. Partly this is due to her wish to live a very private life with her family, whereas Peggy has been visible pretty regularly as a TV sports announcer for the past decades. For whatever reason, Kristi didn't make an immediate splash, though thank goodness she's proved to have staying power. She may be better known today than she was right after her win at Albertville.
Plus, she is one of those rare genetic marvels who get ever the more lovely with each passing year.
Jay Leno thought Michelle was Nancy Kwan (an actress).
Had to laugh re: "little girl on helium!" Hamill really does have a lovely speaking voice; so does Fleming. Hamill has been on TV recently in ads/infomercials for a new exercise machine. The skating fan in me remembers seeing her but can't remember much about the machine!
Tough to narrow it down to just three! But for preference, in each discipline ...
Ladies: Midori Ito (JPN), Michelle Kwan (USA), Yuna Kim (KOR)
Men: Alexander Yagudin (RUS), Daisuke Takahashi (JPN), Brian Boitano (USA)
Pairs: Gordeeva & Grinkov (USR / RUS), Shen & Zhao (CHN), Savchenko & Szolkowy (GER)
Dance: Virtue & Moir (CAN), Davis & White (USA), Torvill & Dean (GBR)
I've chosen skaters who I think became famous also outside figure skating world.
Torvill and Dean
Gordeeva and Grinkov