These are the people that have (or almost have) gotten in Yui's way somehow.
Case #1: Miaka
"Love hates you/ I live my life in ruins for you/ And for all your secrets kept/ I squashed the blossom, and the blossom's dead" -HOLE
Miaka is Suzako no Miko...
Right off the bat, the two are supposed to be enemies. When Yui becomes Seiryuu no Miko, she and Miaka are competing to find their seven Seishi first, for whoever does gets their three wishes granted. Yui hates Miaka most of the time for betraying her (I'm not going to explain why again. You can find it all over this page, but mostly in "General Info"), and when Miaka tells her that Nakago has been deceiving her, Yui-chan accuses her of lying, and runs away. She thinks, "If Miaka is telling the truth, I have no reason to hate her!" and this scares her, because she desperately wants revenge. When Yui calls Seiryuu, her first wish seals the powers of Suzako, and the second wish returns Yui and Miaka to their world so that Miaka can't be with Tamahome. However, her third wish doesn't come until near the very end, when Nakago is about to defeat the remaining Suzako Seishi. Nakago requests for Yui to wish him eternal life, but she wishes for Miaka to be able to call Suzako so that she can save their world. This is a very selfless act, and since it is her final wish, she is consumed by Seiryuu. Miaka's first wish is to get her Yui-chan back from Seiryuu. (^_^). In the end, Yui realizes how lucky she is to have Miaka as her best friend, and she comes to accept Tamahome's love for Miaka. However, Miaka is still a potential enemy, so nah. :Þ
Case #2: Soi
"You have a home in a quiet place/ And someone else feels your strong embrace/ She is protected, and she needs no chase/ And do you love her?" -The Corrs
Soi is a Seiryuu Seishi...
Although she and Yui are not enemies, Soi has reasons to hate her. She has loved Nakago all her life, and would die before she gives him up. See, when she was little, her parents sold her to a brothel to make ends meet. She was about to be attacked by two men, when Nakago saved her. (Sound familiar? Just like what happened to Yui.) After that, Soi fell in love with him, as she knew him for so long. Soi's power is raising a Seishi's Chi (or energy level), which she does by...ahem...making love to that Seishi. She does this several times for Nakago. -_-;; Soi is basically the only one that Nakago is intimate with.
Soi is standing outside the room where Nakago tells Yui he loves her (and kisses her). This makes her extremely jealous and upset, which is why she's a potential enemy of Yui's. However, when Soi dies in battle in Nakago's arms after telling him her feelings, Nakago carries her around on his horse until he can put her to rest (aww...), which is a basic sign that he cared very much for her, otherwise he would have left her body on the battle field.
Well, that's basically it. If you can think of another one of Yui's potential enemies (besides the Suzako Seishi, which is a given) please e-mail me to let me know, and I will give you credit for the idea.