Api design for both web and mobile platforms

When designing a back-end API that will be used by web, mobile or other clients, which approach should I prefer? What are benefits and drawbacks?

• Design separate API for each client
• Design one API for all clients
• Develop web app without API, create an API for mobile/other clients
• ?

Consider these situations

• Different data access level (web app has admin panel, custom reports etc.)
• Performance
• Maintenance
• Extendable