I have read that volatility smiles didn't show up for equity options until 1987. Can some one give me an example(s) of what markets now still don't have volatility smiles and what an explanation for them not having equity smiles would be? thanks
There are tons of market where vol smile doesn't exist - either because no one makes a market on the call/put options (private equity, physical real estate comes to mind) or only the ATM option gets traded infrequently. You can't have volatility smile without a vol market.
On the other hand (and maybe more relevant to what you are trying to get at), if only ATM option market exists for the underlying asset, and someone wants a bespoke/one-off price on a strike other than ATM, then you can also call transactions like this "not priced off of a vol smile". Lets say you want to buy effectively a 25 delta call (keep in mind you are unlikely to have priced delta precisely). Market maker could price this at ATM vol, and tag on an "extra" which expresses his views on what realized vol + friction cost to trade this look like, so that he could hedge himself, and still satisfy your demand as a client.