I laugh at people dismissing the Irina-Michelle rivalry, or saying Michelle was already past her peak when it started. Her performances at the 2000 and 2001 Worlds in the LP were probably her best ever when you consider technical aspects of the skates too. Even her amazing performances at the 1998 U.S Nationals she didnt land a triple-triple, and she was even faster and more dynamic in her 2000 and 2001 Worlds LP. She was spurred to that level of performance due to the incredible opposition offered by Irina those years, and even Maria in 2000 (who remember won the short program at Worlds that year, and was defending World Champion). Irina and Michelle had an intense 3 year rivalry from the 99-2000 season through to the 2001-2002 season. Unfortunately the rivalry was stalled from there due to alternating health problems for both, as well as personal problems for Irina. Irina was even a close competitor of Michelle in 94-96, and despite the beginning stages of her slump was still a close competitor to both Michelle and Tara in 97, before the major problems of the 97-98 and 98-99 seasons.
Maria could be classified as a challenger to Kwan from the 98-99 and 2001-2002 seasons, not a great rival but still a competitive threat to some extent. When Michelle faltered at the 99 Worlds Maria ended up beating her for the title in convincing fashion, also remember Michelle's performance in the 99 LP at Worlds while not perfect was fairly respectable, she landed 6 clean triples, only stepped out of the triple lutz (so even was close to all 7 triples), did not do the triple-triple she had planned, and singled a double axel. Maria still won straight 1st places in the LP, Michelle would have needed to skate her best to have beaten her, which is what I call a legitimate challenge put forth. Maria remember won the short program at the 2000 Worlds over both Irina and Michelle, she couldnt hang on in the LP, but again she was very much challening too. She lost a controversial 5-4 split to Irina at NHK in 2000, which would have made Irina the only one to go undefeated in the GP series in the 2000-2001 season, Michelle losing once and had that decision gone the way most think it should have then Irina also would have, and Maria would have topped both in the GP series. Maria also beat Michelle in the SP in the 2001 GP final. Maria was always lurking throughout that quadrennial, but she wasnt consistent enough, and most times Michelle and Irina were just too strong also.
Cohen I would classify as a Kwan rival too. Kwan had to come from behind to beat Cohen for the title at the 2000 Nationals. Kwan had to fend off an impressive Cohen at the 2002 Natonals, and had to fend off Cohen for a medal at the 2002 Olympics. Cohen was considered Kwan's most serious threat at both the 2003 Nationals and 2003 Worlds. Kwan had to come from behind after the SP to beat Cohen at the 2004 U.S Nationals again and did. Cohen then beat Kwan at the 2004 Worlds. Kwan beat Cohen to tie the record for U.S titles at the 2005 U.S Nationals, then Cohen again beat her at Worlds. That was a rivalry.
Even Hughes was a mini rival of sorts.
Kwan had many impressive rivals and she stared them all down. She actually had more challengers after Tara left then when Tara was there, where for awhile it was only Tara. Also even Tara she was thought to only have any chance of losing to with major falls, that was until the shock of Nagano. Tara's other wins were all when Michelle had multiple more and more serious mistakes and Tara was squeeky clean.