It seems that many people donโt realize that the only time โitโsโ is needed is when the words โitโ and โisโ (or โhasโ) are being contracted. (โItโsโ = โIt isโ or โIt has.โ The word โitsโ signifies possession, and needs no apostrophe. (Nor do these words need one: yours, his, hers, theirs, and ours.) I guess the confusion stems from the fact that the apostrophe is used to show possession by a noun, as in โthe flowerโs petals.โ
Inspired by fred.net.
Update: fred link still good. (Nov. 2013)