Blue Submarine No. 6, to Under the Sea from A*Teens. Just 'cause it'd be funny.
Sesshoumaru & Rin (from InuYasha), to Phil Collins' You'll Be In My Heart from Tarzan.
Specifically:
"Don't listen to them
'Cause what do they know?"
Could go with the (subtitled) scene after Totosai explains that Tetsusaiga can only be used in defense of humans, and InuYasha says that Sesshoumaru isn't capable of feeling protective toward anything (or something similar; it's been a while)
InuYasha's Torment and Redemption, to Phil Collins' No Way Out (Single version) from Brother Bear
Everywhere I turn, I hurt someone,
(InuYasha pushing Kagome aside in the second movie)
but there's nothing I can say to change
the things I've done.
(blood on his hands, after massacring the village when he went full-demon)
Of all the things I hid from you,
(Kagome witnessing the InuYasha/Kikyo kiss)
I cannot hide the shame,
(In the river with bloody hands, sobbing, with Kagome watching)
and I pray someone, something will come
to take away the pain!
(shot through the heart)
(chorus)
There's no way out of this dark place.
No hope, no future.
I know I can't be free,
but I can't see another way.
I can't face another day.
Tell me where did I go wrong.
(Inu-pup, running to his mother)
Everyone I loved, they're all gone.
(Kikyo collapsing and dying)
I'd do everything so differently,
but I can't turn back the time.
(Naraku-InuYasha walking away from the fallen Kikyo)
There's no shelter from the storm
inside of me.
(any full-youkai transformation)
(chorus repeat)
I can't believe the words I hear.
(after the massacre, Kagome's hand on his shoulder)
It's like an answer to a prayer.
When I look around I see
this place, this time, this friend of mine.
(the sengoku jidai, Kagome)
I know it's hard, but you found somehow,
(Kagome in the present, realizing that she loves him)
to look into your heart, and to forgive me now.
(running to hug him)
You've given me the strength to see
(he smiles)
just where my journey ends.
(in the present, posing after killing the Noh mask)
You've given me the strength to carry on.
(as a full-human, confronting Kouga, unashamed)
I see the path from this dark place.
I see my future.
Your forgiveness has set me free.
Oh and I can see another way;
I can face another day!
I see the path, I can see the path
I see the future
I see the path from this dark place
I see my future
(etc)
Over the end would go a bunch of scenes from "heroic" InuYasha, like helping Kagome, helping Bunza defeat the barrier, rescuing Shiori, generally being heroic and noble.
And it's not actually animé, but:
The new TMNT series to the "Turtle Rhapsody" from the old TMNT movie (that rap/trumpet thing that was in the first two films)