EAI is Enterprise Application Integration. 

Tools used are: WebSphere ICS, WebSphere MQ series,
WebSphere Application Server, Tibco, Seebeyond, Vitria etc.

also IBM product  DATAPOWER XI50

Why isn't Biztalk been listed? :(

EAI = Enterprise Application Integration.
Tools: Biztalk, Webmethods, SeeBeyond, TIBCO, Vitria etc

EAI is Enterprise Application Integration. 

Tools used are: WebSphere ICS, WebSphere MQ series,
WebSphere Application Server, Tibco, Seebeyond, Vitria etc.
 SAP XI.

Enterprise Application Integration (EAI) is the integration 
of new application software such as middleware tools with 
existing software which provides the functionality that 
supports the enterprise’s business processes. 

A framework which allows rapid development and Reuse of 
interfaces among Disparate enterprise systems by achieving 
isolation of business logic and improved administrative 
control.

There are basically two architecture HUB & SPOKE/BUS. Based 
on that various integration tools are vailable in the 
martket. Few of them are-

1) Hub & Spoke architecture- WebMethods – Integration 
Platform, Vitria Technology – BusinessWare, WBI – 
Collaborators, Connectors  
2) Bus architecture- Tibco Active Enterprise , SeeBeyond 
eGATE Integrator