Linq to objects, in 580 characters (without whitespace)
Console.WriteLine(Enumerable.Range(1, 13).SelectMany(day =>
Enumerable.Repeat("\nOn the " + day +
(day == 1 ? "st" :
(day == 2 ? "nd" :
(day == 3 ? "rd" :
"th"))) + " day of Christmas my true love gave to me ", 1)
.Concat((new []
{
"twelve drummers drumming,",
"eleven pipers piping,",
"ten lords a-leaping,",
"nine ladies dancing,",
"eight maids a-milking,",
"seven swans a-swimming,",
"six geese a-laying,",
"five gold rings,",
"four calling birds,",
"three french hens,",
"two turtle doves, and",
"a partridge in a pear tree."
}).Reverse().Take(day).Reverse()))
.Aggregate((a, b) => a + "\n" + b));