Multiple API's
See Rest API Vs SOAP API in Salesforce - Salesforce Stack Exchange for some links to some in depth documentation.
Metadata API
using tools like Mavens Mate (See MavensMate and Git for Non Developers).
Tooling API
Chatter API
A lightweight REST API to just use Chatter.
Streaming API
Replaces batch jobs.
Data is pushed to the API whenever it changes.
Like push notifications on your phone.
Be very careful of passing your data from your Salesforce org to third party services via URLs.
Turn off the API Enabled permission for users that don't need it.
However, In practice this can be quite limiting because many many apps use the API.
Block individual apps. See this great post by Cloud Sherpas on monitoring and blocking Apps Managing External Apps with Connected Apps - Cloud Sherpas
As a SF Admin you need to monitor all apps that have a connection to your Org.
Setup > Manage Apps > Connected Apps OAuth Usage.
Your Name > Personal > Connections shows the apps that each user is connected to.
But that is not the full story - there may be apps that are connected via token.
Be aware of any apps that are connected via a token.
If necessary:
Articles about the Salesforce API.