HTTP defines a bunch of meaningful status codes that can be returned from your API. These can be leveraged to help the API consumers route their responses accordingly. I've curated a short list of the ones that you definitely should be using:

200 OK - Response to a successful GET, PUT, PATCH or DELETE. Can also be used for a POST that doesn't result in a creation.
201 Created - Response to a POST that results in a creation. Should be combined with a Location header pointing to the location of the new resource
204 No Content - Response to a successful request that won't be returning a body (like a DELETE request)
304 Not Modified - Used when HTTP caching headers are in play
400 Bad Request - The request is malformed, such as if the body does not parse
401 Unauthorized - When no or invalid authentication details are provided. Also useful to trigger an auth popup if the API is used from a browser
403 Forbidden - When authentication succeeded but authenticated user doesn't have access to the resource
404 Not Found - When a non-existent resource is requested
405 Method Not Allowed - When an HTTP method is being requested that isn't allowed for the authenticated user
410 Gone - Indicates that the resource at this end point is no longer available. Useful as a blanket response for old API versions
415 Unsupported Media Type - If incorrect content type was provided as part of the request
422 Unprocessable Entity - Used for validation errors
429 Too Many Requests - When a request is rejected due to rate limiting