Bash / Sed, <strike>705</strike> 697 chars
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A pretty simple solution, based on the significant repetition in the song.<br>
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 gameQwe'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 aroundQdesertU\nNmakeU cry\nNsay goodbye\nNtell a lieQhurtU/g;\
    s/E/Ngive, never gonna give\n(GV/;\
    s/V/iveU up)\n/g;\
    s/U/ you/g;\
    s/Q/ and /g;\
    s/N/Never gonna /g"<<Q
    We're no strangers to love
    You know the rulesQso 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