[Daycrawler]

It depends on the use-case.

* Public data API (no notion of user account, e.g. weathers API, newspapers API, GitHub public events, Reddit /r/popular, etc): use an API key. The developers must create an account on your website to create their API key; each API call is accompanied by the API key in the query string (?key=...)

* Self-used API for AJAX (notion of user account, e.g. all the AJAX calls behind the scenes when you use Gmail): use the same user cookie as for the rest of the website. The API is like any other resource on the website except it returns JSON/XML/whatever instead of HTML.

* Internal API for micro-services: API key shared by both ends of the service. There can be a notion of user accounts, but it's a business notion and the user is an argument like any other. If possible, your micro-services shouldn't actually be accessible on the public Internet.

* API with the notion of user accounts intended for third-parties (e.g. Reddit mobile app where the users can authorize the app to use their Reddit account on their behalf): OAuth2