Another C#
var l="a partridge in a pear tree.|two turtle doves, and|three french hens,|four calling birds,|five gold rings,|six geese a-laying,|seven swans a-swimming,|eight maids a-milking,|nine ladies dancing,|ten lords a-leaping,|eleven pipers piping,|twelve drummers drumming,".Split('|');
for (int i = 1; i < 13; i++)
Console.Write(
"On the {0}{2} day of christmas\rmy true love gave to me \r{1}\r\r",
i,
string.Join("\r", l.Take(i).Reverse().ToArray()),
(i==1?"st":i==2?"nd":i==3?"rd":"th"));
Borrowed heavily from previous answers (hey, code reuse) while adding extra savings.
481 characters once you take out unnecessary whitespace:
var l="a partridge in a pear tree.|two turtle doves, and|three french hens,|four calling birds,|five gold rings,|six geese a-laying,|seven swans a-swimming,|eight maids a-milking,|nine ladies dancing,|ten lords a-leaping,|eleven pipers piping,|twelve drummers drumming,".Split('|');for(int i=1;i<13;i++)Console.Write("On the {0}{2} day of christmas, my true love gave to me \r{1}\r\r",i,String.Join("\r",l.Take(i).Reverse().ToArray()),(i==1?"st":i==2?"nd":i==3?"rd":"th"));