Do you mean headphones, or in-ear phones? Many brick & mortar shops will let you try on headphones in a demo area setup for that purpose. Bose has their own demo tables they provide to some stores for the purpose of demonstrating their noise cancelling headphones, amongst other products. [That's how I got hooked - the store let me plug in my own phone into their demo unit, so I could see how they sounded on my own favorite songs.]
I don't know of anywhere that will let you try earbud headphones, for hygiene reasons.
The big electronics retailers in Tokyo let you try earbud headphones; they usually have most of their range on display with the jacks available to plug into your phone. There's alcoholic wipes to clean the buds.
I don't know of anywhere that will let you try earbud headphones, for hygiene reasons.