1xx informational, 2xx success, 3xx redirection, 4xx client error, 5xx server error. The first digit gives you the broad category; the rest narrow it down.
The codes you'll actually use: 200 OK, 201 Created, 204 No Content (success); 301 Moved Permanently, 304 Not Modified, 307 Temporary Redirect; 400 Bad Request, 401 Unauthorized, 403 Forbidden, 404 Not Found, 422 Unprocessable Entity, 429 Too Many Requests; 500 Internal Server Error, 502 Bad Gateway, 503 Service Unavailable.
The full list including weird ones (418 I'm a teapot, 451 Unavailable for Legal Reasons) is at /tools/http-status-codes.