1. Joda-Time :- An easy replacement for the official Java date/Time classes. Many are suffering from the bad design of the official date/time.
This library helps you to solve almost every date/time issue faced by java developer.
http://joda-time.sourceforge.net/

2.Apache-Commons:- An extension to theĀ  Core functionality of Java.

a)BeanUtils:- Provides methods to handle the Beans. eg: BeanUtils.copyProperties(targetBean,sourceBean); to copy the values of similar properties.
b)Lang :- Provides extra functionalities to handle the java.lang classes. eg: StringUtils.isEmpty(str);

3.Google Guava :- Something similar to Apache commons.

4.Apache Lucene (http://lucene.apache.org/) : A must-have library for indexing. Add Lucene to speedup your searching.

5.iText:- For PDF processing

6.Apache POI :- For Processing various file formats like word,spreadsheet,Open XML standards etc.