As you mentioned JDBC, this API connects to (typically) database engines such as Oracle, IBM's DB2, MS's SQL Server, HSQLDB, etc. But because the API can be implemented by anyone, I have heard of it being used as a way to access non-relational data stores through SQL queries.
CORBA - Java SE includes CORBA API to connect and execute methods of objects written in other languages and running in other processes (other computers). This has often been used to call C++ and Ada applications/services.
Web Services - Java can connect and invoke services provided by other server applications via HTTP. Libraries that implement SOAP and REST APIs include fundamental packages in Java SE and EE core librairies, Apache Axis2, etc.
Native libraries - Java Native Interface (JNI) is a way to wrap calls to C and C++ native libraries (compiled for a specific operating system/host architecture). Java Native Access (JNA) is a newer approach to doing the same, not involving a lot of boilerplate and glue code like JNI does.
Scripting Language Code - the javax.script package supports calling external script code (conceptually very similar to JDBC), so you can call Ruby, Python, Javascript code, etc. You can also use Jython, JRuby, rjb (Ruby Java Bridge), and other langauge-specific connectors.
JNDI (Java Naming and Directory Interface) - partly included in Java SE, fully included in JEE, provides support for connecting to LDAP and DNS services, for example MS Active Directory services.