Most wired headphones have 3.5mm plugs. RunPhones® Classic headphones also have a 3.5mm plug. If your device has a standard round port, you should be able to use any headphones without an adapter.
A select group of manufacturers began eliminating the round 3.5mm port from their devices a few years ago. Anyone with those devices needs an adapter to use any headphones that have a 3.5mm plug.
If you need a Lightning adapter to connect wired headphones to your iPhone, you can buy one right here: