-Virtually unlimited buyers and sellers - any industry which has seen significant corporate consolidation is out
-No barriers to new sellers opening up shop - anything which requires major investment in infrastructure or equipment doesn't count
-Complete transparency of information - the internet has gone a long way to providing this one - in the past this one made the entire idea purely hypothetical.
So, score one for Free Markets.
-Zero transaction costs - any purchase made by credit card isn't a free market transaction. Also all financial industry transactions, stocks purchases, loans, by definition, don't operate in a free market
-Rational buyers - the entire $44 billion advertising industry is devoted almost entirely to preventing rational buyers. Pre-Edward Bernays advertising was generally of the format: "This product exists. These are its features. This is what it costs." Post-Bernays marketing is about using psychology to manipulate individual behavior; getting people to buy something which they wouldn't without the ad, even if they knew about it.
-No externalities - anything that produces pollution or draws on common goods can not be claimed to operate in the free market.
Obviously that doesn't leave much left.