The Sailor Senshi:  "Angels Among Us", by Alabama.

Shinji Ikari:  "Under Pressure", by David Bowie and Queen.

Rei Hino:  "Eternal Flame", by the Bangles.  (Obvious one, really.)

Ayeka:  "Waiting For You", by Celine Dion.

Usagi:  "Standing Outside the Fire", by Garth Brooks.

	("We call them weak,
	  Who are unable to resist,
	  The slightest chance love might exist,
	  And then for that forsake it all.")

	or possibly "What If God Was One of Us?" by Some Singer Whose Name
	I Can't Remember And For Which I Have Spent Twenty Minutes
	Futilely Searching the WWW.

Mamoru (second arc of Sailor Moon R):  "Vicki Waiting" by Prince.

Priss:  "Our World, Our Times", by Alannah Myles.

Asuka Soryuu Langley:  "Crucify", by Tori Amos.

Sylia:  "Tales From The Future" by Vangelis.

Sheila Tenkai:  "The One", by Elton John.

Noboyuki:  "The Last Song", by Elton John.

Billy Fanward:  "One", by Metallica.

Washuu:  "Weird Science", by Oingo Boingo.

Gendou Ikari:  "Cold Hearted Snake", by Paula Abdul.

Ranma:  "Probably Me", by Sting.

Yurika:  "Nothing's Gonna Stop Us Now", by Jefferson Starship. 
(Gratuitous Plug:  Martian Successor Nadesico.  Like Evangelion, but
funnier.)

Tenchi:  "Glory of Love", by Peter Cetera. (Cliched as hell, but what are
you gonna do?)

Miyu:  "Love Song For A Vampire", by Annie Lennox.  (Ditto)

Tsubasa:  "Sweet Transvestite", from the Rocky Horror Picture Show.
(*Somebody* had to say it.)

Skuld:  "Hammer Time", by M.C. Hammer.  (Ditto)

Chris Davies.