The first category is algorithms as a service, where you are provided with an API or even graphical user interface to connect preprogrammed components of data science pipeline together:

• Google Prediction API: It was one of the first companies that introduced prediction services through its web API. The service is integrated with Google Cloud Storage serving as data storage. The user can build a model and call an API to get predictions.
• BigML: It implements a user-friendly graphical interface, supports many storage providers (for instance, Amazon S3) and offers a wide variety of data processing tools, algorithms, and powerful visualizations.
• Microsoft Azure Machine Learning: This provides a large library of machine learning algorithms and data processing functions, as well as graphical user interface, to connect these components to an application. Additionally, it offers a fully-managed service that you can use to deploy your predictive models as ready-to-consume web services.
• Amazon Machine Learning: It entered the market quite late. It's main strength is seamless integration with other Amazon services, while the number of algorithms and user interface needs further improvements.
• IBM Watson Analytics: It focuses on providing models that are already handcrafted to a particular domain such as speech recognition, machine translations, and anomaly detection. It targets a wide range of industries by solving specific use cases.
• Prediction.IO: It is a self-hosted open source platform, providing the full stack from data storage to modeling to serving the predictions. Prediction.IO can talk to Apache Spark to leverage its learning algorithms. In addition, it is shipped with a wide variety of models targeting specific domains, for instance, recommender system, churn prediction, and others.

Predictive API is an emerging new field, so these are just some of the well-known examples; KDnuggets compiled a list of 50 machine-learning APIs at http://www.kdnuggets.com/2015/12/machine-learning-data-science-apis.html.