Spring/CDI, JPA/Hibernate/ibatis, webframeworks/JSF/SpringMVC/Struts/Vaadin/
Play, JQuery(not java, but almost a must if you want to be web developer),
AOP(you need to know). restlet(if you want to do rest API development)
basically, web mvc, persistence, web service. Spring is a must, but you dont
start from spring. You can start from spring mvc, then connect to database
with JDBC, then you learn hibernate/JPA, then use spring to enhance what you
have. 2 or 3 months, you would have a solid java ee small project codebase,
if you want more, then make it restful with spring mvc or make it a service
thing use restlet.
After this, if you want more, try activitie, solr, tika, i am not sure
alfresco, ofbiz, liferay qualified as framework or not, but no harm have a
look.