Which are the all API's that are compatible and integrable with discourse

[blake (Blake Erickson)]

There isn’t an exhaustive list available for API integrations. Depending on what you are trying to do there might be support for it in core like sendgrid for email, or oauth2 for authentication. For other integrations like Zendesk there is likely a plugin for it. Is there something else other than Discourse Integration with Google Cloud Search that you are interested in?