Sharing data between two or more server based systems is the key feature of cloud computing. Building an API around your database or specific tables is a serious point in modern Application and Web-Development. Web service API's must be as agil and scalable as your Application and Software environment. Without a solid concept and integration of best practices you can get into serious trouble when your upcomming API is in action and run into errors or is not scalable enough. We build robust services and RESTful API's with PHP or C / C++.
PHP with its direct connection to JSON and XML is great for developing, active testing and the delivery of web services. When we talk about RESTful, RPC or SOAP services, we talk about HTTP request and resonse process inside or outside a client session. The "best" web services are services which deliver more than one data scheme, for example XML and JSON.
In fact RESTful API's had become the bread and butter paradigm for web services worldwide. When you call a eCommerce, eBusiness, Portal, Application, Software or Hardware Company and ask after their application programming interface, they say to 90% "We offer REST". The reason why most companies go with RESTful API's is because you can use them in the Intra- and Internet and also in many hardware based projects, products and solutions like the Raspberry Pi.
There are many frameworks, tools and techniques for developing, implementig and debugging web services arround your product. I call this object "product", because from the agile point of view, a micro CMS can become an Enterprise CRM system within years. This fact depends on the attributes and functional needs of the project and customers.
Beside the web service API development and integration we have the documentation, which is immensely important for you and the client or user. The documentation is the reflection of your web service and shows the consumer, if you have done your job right. Often external developers implement the consuming part on the customer side and need a 100% clear API definition from you, cause they want deliver a robust and most important secure service.