All classes in Java standard library are important but here is the list of frequently used packages and classes.

1. java.lang – This package is imported by default in all Java classes. It contains basic classes required to run a simplest program. Some of the most frequently used classes in this package are – String, Integer, Double etc
2. java.util – contains classes for Calendar, Date,Regular Expression related classes and various collections like List, Vector, Map, Dictionary, Set, Queue, Stack etc
3. java.io and java.nio – This package has got classes to interact with file system. java.io is used when dealing with stream oriented and blocking input output. While java.nio is used when dealing with buffer oriented and non blocking input output.
4. java.net – This package contains classes required to access resources over network and internet
5. java.awt and javax.swing – GUI applications
6. java.text – formatting of numbers and strings
7. java.applet – creating applets that run in browser