Are anime OP/ED theme songs original? Are anime OP/ED theme songs original? Is it like after creating an anime, the producer hires a singer to sing a song for the OP/ED theme for that anime, or do they just use songs that the singer already sang for his album or something like that?
The vast majority of the time (easily upwards of 95% of the time, by my estimate), OPs/EDs are produced specifically for the anime they're used in. Reuse of existing songs is rare. 

There are counterexamples, though, which by their very rarity prove the rule. A few select examples:


Erased reused Asian Kung Fu Generation's 2004 song "Re:Re".
JoJo's Bizarre Adventure (2012 version) reused Yes's 1968 song "Roundabout".
Speed Grapher reused Duran Duran's 1981 song "Girls on Film". (Thanks, @ConMan.)
One Week Friends reused Sukima Switch's 2004 song "Kanade", though in this case, it was re-recorded with Amamiya Sora (voice actor of the character Fujimiya Kaori) as the vocalist.
And, of course, Neon Genesis Evangelion uses a great many different recordings and mixes of the classic "Fly Me to the Moon" as its ending theme.