Bash / Sed, 705 699 chars
A pretty simple solution, based on the significant repetition in the song.
Line breaks within the sed command are not needed, characters are counted without them.
sed \
"s/L/ \nWe've known each other for so long\nYour heart's been aching but\nYou're too shy to say it\nInside we both know what's been going on\nWe know the game and we're gonna play it/;\
s/T/I just wanna tellU how I'm feeling\nGotta makeU understandR/;\
s/R/\n \nNgiveU up\nNletU down\nNrun around and desertU\nNmakeU cry\nNsay goodbye\nNtell a lie and hurtU/g;\
s/E/Ngive, never gonna give\n(GV/;\
s/V/iveU up)\n/g;\
s/U/ you/g;\
s/N/Never gonna /g"<<Q
We're no strangers to love
You know the rules and so do I
A full commitment's what I'm thinking of
You wouldn't get this from any other guy
T
L
And ifU ask me how I'm feeling
Don't tell meU're too blind to seeRR
(Ooh, gV(Ooh, gV(Ooh)
E(Ooh)
EL
TRR
Q