Postman - The Collaboration Platform for API Development
apiman - Open source API management
Django REST framework - Django REST framework is a toolkit for building web APIs.
WSO2 API Manager - WSO2 API Manager is a 100% open source enterprise-class solution that supports API publishing, lifecycle management, application development, access control, rate limiting and analytics in one cleanly integrated system.
Amazon API Gateway - Create, publish, maintain, monitor, and secure APIs at any scale
Gravitee.io - Gravitee.io is a flexible, lightweight and an open source API management solution.