Composer Yuki Kajiura is responsible for many memorable anime themes and background music. Also, she sometimes collaborates with a singer or a group of singers to form her "solo" project, FictionJunction.
Most of Noir's soundtrack is composed by Yuki Kajiura and is pretty amazing absolutely fucking brilliant.
Canta Per Me from Noir. You've got a somewhat melancholy romance song, sung by a Japanese woman in Italian, mostly used to score either awesome shootouts or the buildup to awesome shootouts, and somehow it just works.
Mai-Hime and Mai-Otome have three (Mezame, Materialize and Sei Otome no Inori) of these between them, and all the rest of the soundtrack is just as good. And none of them even have any (comprehensible) lyrics.
How can you talk about Tsubasa music without mentioning Ship of Fools?
In fact, the music is so amazing, that it nearly makes up for the epic fail that is the Bee Train anime adaptation of Tsubasa. That is REALLY saying something. This troper would like to add Smile (Fai's Image Song) and Hear Our Prayer. The latter is truly heartbreakingly beautiful.
Sacrifice also shows how awesome the Tsubasa soundtrack really is.
This troper would like to add Synchronicity due to its sheer epicness, as well as I Talk To The Rain, because if this song doesn't move you is because you don't have a soul.
Femme is utterly haunting and gorgeous. Morning Moon deserves a mention too, for being able to pack so much emotion into such an understated song.
So you're watching Kara no Kyoukai. Hear any strings? Is it the main theme? Or an instrumental rendering of any given ending song? Prepare for asskicking of barely comprehensible proportions.
Submitted for your consideration here, here, here, here, and here (the best for last).
And I challenge any man here, Brother Martial Artists and Warriors in particular, to not shed Manly Tears at 1:01 of "Lightseekers" as the thunderous chorus of Kenshiro's theme fills his heart with courage and his soul with hope.
Open Your Heart Particularly the Fiction Album version is also a beautiful song.
"In the Land of Twilight, Under The Moon" is a wonderfully composed song that fleshes out a very descriptive atmosphere primal, chaotic, and hedonistic urges and celebrations through it's lyrics and chaotic use of saxophone and guitar riffs. There is nothing you can't like about this song.
"Aura" is an absolutely haunting theme that perfectly portrays Morganna's plotting regarding the birth of Aura, showing both the dark and light sides of "The World".
The entire soundtrack of Le Portrait de Petite Cossette amounts to this, but the Main Theme is probably the best example, if only for its use at the end of the series when Eiri uses his own blood to paint a portrait of Cossette in order to defeat the spirit of the grudge contained in the portrait that Cossette's murderer painted of her, which was why he killed her.
The original posting troper is partial to Ghost Blood, Cradle, Another Dimension, Revolve, and Misgiving, in addition to the already-mentioned Will and Contractor. But still, nothing beats Every Time &c.
Her work in video games shouldn't be ignored either. Particularly on her work in the Xenosagagames.
Kajiura has been confirmed as being the composer for the music of Fate/zero. Just the first PV alone is enough to give you an eargasm, and now that the first episode has been released we can safely confirm the score will not disappoint.
It's a travesty that the second opening, to the beginning and the second ending, Sora wa Takaku Kaze wa Utau aren't on here. Especially since they were both composed by her.