java.lang Used all the time. String may be the most frequently used class of all
In beginners' code, 99% of the API classes used will probably come from those packages.
Avoid packages whose names start with com.sun or similar; those classes might be changed in the future. Don't go through packages reading all the classes, but look for the classes you think you might need and look at their API documentation.
It's difficult to answer that question, because what packages you need depends on what kind of software you are writing. For example, if you are writing a desktop application or an applet, then you most likely use the Swing and AWT packages (javax.swing and java.awt), but if you're writing server-side software that doesn't have a GUI then you don't need those.
Ofcourse, the classes in java.lang and java.util are the most used packages from the standard Java API.
Depending on what you're doing, I might add java.math and java.text to the list. But as already mentioned, a beginner is not going to stray much outside of java.lang and java.util, and the list of other packages you're likely to use is a lot smaller than you think. So don't let the API intimidate you.
"We're kind of on the level of crossword puzzle writers... And no one ever goes to them and gives them an award." ~Joe Strummer sscce.org
I think the first two will be true for eveyone, and after that it really depends on what sort of jobs you get hired to do. As a beginner, I'd just focus on the first two. [ December 21, 2007: Message edited by: Jim Yingst ]