Out of curiosity I ran two Google searches this morning, whose results were surprisingly close:

Results 1 – 10 of about 801,000 for "free reign"
Results 1 – 10 of about 841,000 for "free rein"

The right one won, but only just. This gave me an idea for a couple of silly Google challenges, if anyone reading this is bored enough:

Firstly, see if you can find a well known word or phrase, together with a common misspelling, in which the wrong spelling actually gets more hits on Google. (Cross-channel variation, or other reasonably justifiable differences of opinion, don't count as misspellings. One of them has to be clearly wrong, such that anyone sufficiently educated who isn't an incurable descriptive linguist has to agree on which one it is.)

Secondly, see if you can find a wrong-and-right pair in which the scores are (proportionately) closer together than the above two.

I haven't tried either, but I'd guess the second challenge would be harder than the first: I'm sure there must be some wrong spelling more popular than the right one, but those two are really pretty close by the normal Google standards (there's usually more like an order of magnitude difference).