The ASF is made up of over 100 top level projects that cover a wide range of technologies. Chances are if you are looking for a rewarding experience in Open Source, you are going to find it here.
A network application framework
Apache MINA is a network application framework which helps users develop high performance and high scalability network applications easily. It provides an abstract, event-driven, asynchronous API over various transports such as TCP/IP and UDP/IP via Java NIO.
The Apache Cassandra database is the right choice when you need scalability and high availability without compromising performance.
Linear scalability and proven fault-tolerance on commodity hardware or cloud infrastructure make Apache Cassandra the perfect platform for mission-critical data. Cassandra's support for replicating across multiple datacenters is best-in-class. Cassandra is in use at Netflix, Twitter, Urban Airship, Constant Contact, Reddit, Cisco, OpenX, Digg, CloudKick, Ooyala, and more companies that have large, active data sets. Cassandra provides full Hadoop integration, including with Pig and Hive.
Apache Axis2 is a service hosting and consumption framework that makes it easy to use SOAP and Web Services
Apache Axis2 is a toolkit for creating and using Web Services, including SOAP, MTOM, XML/HTTP and advanced WS-* standards such as WSRM and WSSecurity. Axis2 includes a very fast runtime engine, together with tooling support for WSDL and WS-Policy, and plugin support for WS-Addressing, WS-ReliableMessaging, WS-Security, WS-Eventing, WS-Transactions, WS-Trust and WS-SecureConversation. Axis2 runs either standalone or hosted in Tomcat or other servlet containers.