Here's my shortest attempt in Ruby at
72 characters.
s="Happy Birthday to you,\n";puts s+s+s[0,15]+"dear name!\n"+s[0,21]+'.'
And some other ideas that are longer.
s="Happy Birthday to you,";[s,s,s[0,15]+"dear name!",s.chop+'.'].each{|l|puts l}
s="Happy Birthday to you,";puts [s,s,s[0,15]+"dear name!",s.chop+'.'].join("\n")
s="Happy Birthday to you,\n";puts s+s+s[0,15]+"dear name!\n"+s.chop.chop+'.'
s="Happy Birthday to you,\n";puts s+s+s[0,15]+"dear name!\n"+s.sub(',','.')
Fun stuff!