By far the most familiar Yu Yu Hakusho yaoi pairing is HieixKurama. While I can see why people would believe this, I do not support it. And that isn't just my obsession with Kurama talking either. I happen to be a big fan of stories that pair Kurama with Kuronue or Yuusuke, so it's not that I want to keep him for myself. (Which I do, but that's beside the point. ^_~)

A while ago I happened to stumble upon a site devoted to those who are anti-HieixKurama. It's called, logically enough, "Kurama and Hiei: It's Not Love". There I found a good list of reasons as to why these two aren't necessarily a pair. I'll post it here, with my own comments added in (()), but all credit for this list goes to It's Not Love's creator.

Opinion: When they fight, a lot of the time they're really close to eachother.
If you were surrounded by enemies, wouldn't you want to have someone to guard your back? The most effective way to do that is to stand close to that person.
((And on the same note, if you use that argument, Yuusuke and Kuwabara must be lovers too. And so must Inuyasha and Miroku from Inuyasha. O_o))

Opinion: They're always together in pictures.
Well, Chibiusa and Hotaru from Sailormoon are seen together a lot in pictures... so are Raphael and Michael from Angel Sanctuary. They're best friends, so why not show them together? Also, Kurama and Hiei, in my opinion, have the best character designs of the YYH cast. It's only natrual that they end up together.
((Again, there's the Yuusuke and Kuwabara element here.))

Opinion: They sing together in songs.
Um, yeah...but what does that prove? "Eye to Eye" is sung by Kurama, Hiei, and Kuwabara...so...now we have a love triangle? Oh, and about how in that song, Hiei says "I can get you" and then Kurama says "You can get me", I swear I heard Kurama's voice (well...Ogata Megumi, to be more precise) say both lines in the dancemix. I'm sure you'll agree with me when I say that a narcisist is the last thing Kurama would be. There are tons of songs sung by the entire Urameshi Team, so we have a love square? "Mienai Mirai" is sung by Kurama, Hiei, Yuusuke, Kuwabara, Keiko, Yukina, Botan, and Koenma. Does that mean that the whole cast of YYH is a huge love octogon?
((One of the most non sequitur arguments I've ever seen. Since when does singing a duet equate romantic love? Somebody's grasping at straws here.))

Opinion: Hiei's just hiding his feelings with his indifference and coldness.
Have you ever noticed that Hiei acts like that with everyone? Does that mean he has feelings for all the characters in YYH? Oh, and Kuwabara's picked on by Hiei more than anyone, so that means Hiei's completely in love with him?
((And going in the same vein, Hiei is probably the most open and friendly with Kurama.))

Opinion: Opposites attract, and Kurama and Hiei are definately opposites.
I find the personalities of Hiei and Youko Kurama to be quite similar. They both have a bit of that erie calmness, and both are confident in their abilities, sometimes to the point of arrogance. Both can kill without mercy. As for Shuuichi, I see his opposite as being someone more along the lines of clumsy and bubbly, rather than cold and (seemingly) heartless.
((What more can be said here? They're not so opposite as people would think.))

Opinion: You're just homophobic.
Me? Homophobic? O.O Um...I'm a self-proclaimed yaoi fangirl... If you know anything about me, you know that my 3 favorite pairings are Fuuma a Kamui [X], Seishirou x Subaru [X], and Tsuzuki x Hisoka [Yami no Matsuei] O.O;;; The difference? These couplings have at least some valid implications, Kurama x Hiei doesn't. Infact, Kurama x Hiei doesn't even have a definate seme and uke O.o;;;
((This one's really funny to me, considering the fact that I have an obsession with Kurama and I'm a male.))

Opinion: You don't want to see Kurama and Hiei as a couple.
O.o actually...I don't even mind the pairing myself. I just dislike it that everyone takes their "love" as fact.
((Okay, maybe this is a little true. I don't particularly like this pairing, and it also irritates me that, like was said, everyone seems to consider their 'love' a fact.))

Opinion: There's no proof that Kurama and Hiei aren't a couple.
Actually...the creator of Yu Yu Hakusho, Togashi Yoshihiro-sensei, has declared that he didn't intend for the two to be a couple. If the creator says something, isn't it automatically true? His word on the matter shouldn't be ignored simply because you don't agree with it. Anyhow, shouldn't one assume that a pair of characters aren't a couple until proven otherwise, and not the other way around?
((P.S. There's no real proof that they are a couple either.))