To be clear, the situation is different in business and in economy.

In economy, all international aircraft AFAIK are equipped with single-prong 3.5mm headphone jacks and no adapter is needed.

In business, though, most seats are equipped with three prong proprietary plugs designed to operate Delta's noise cancelling headsets (and to prevent them from being useful outside the aircraft). For these ports, a two prong adapter works fine (a connection to the third prong is not needed).

On some airplanes, you can even plug a normal 3.5mm headset into one of the three sockets and it will work correctly in stereo, but you shouldn't depend on that - bring an adapter to be safe.

Note that Delta is no longer packaging adapters with the economy class headsets, so make sure to bring your own if you think you may want one - you no can't ask an F/A for a Billboard pouch to score one onboard anymore.