Bash / Sed, 705 683 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'veKn each other for so long\nYour heart's been aching but\nYou're too shy to say it\nInside we bothK what's been going on\nWeK the game+we'reZplay it\n/;\
s/T/\nI just wanna tellU how I'm feeling\nGotta makeU understandR/;\
s/R/\n \n~giveU up\n~letU down\n~run around+desertU\n~makeU cry\n~say goodbye\n~tell a lie+hurtU/g;\
s/E/(Ooh)\n~give, neverZgive\n(GV/g;\
s/V/iveU up)\n/g;\
s/U/ you/g;\
s/+/ and /g;\
s/K/ know/g;\
s/~/NeverZ/g;
s/Z/ gonna /g\
"<<Q
We're no strangers to love
YouK the rules+so do I
A full commitment's what I'm thinking of
You wouldn't get this from any other guyT
LAnd ifU ask me how I'm feeling
Don't tell meU're too blind to seeRR
(Ooh, gV(Ooh, gVEEL TRR
Q