My personal favorite when I think of a great anime song would have to be Ghost In The Shell, Both Stand Alone Complex and Second Gig.

Here are a few OP's and ED's that I could never skip because I liked them so much.

Heres a classic thats totally un-skippable :P

FLCL = <3

Bleach - Opening 1 - Asterisk (Orange Range)

I go with this

Really my favorite are the ones that are already posted. Paranoia agent and ghost in the shell ones and elfen lied from a musical stand point.

but... really, I'd have to put Zankoku Na Tenshi No by Yoko Takahashi from evangelion as the most memorable for me. Plus I sang this with my friends in japan. Twas fun :P
As well as Escaflowne's opening.

I love this one :)

that's one of my favorite anime... meaning top 3, err 3rd favorite.!