Take particular note of the sections 2) License to use: "Sun grants you a non-exclusive, non-transferable, limited license without license fees to reproduce and use internally Software complete and unmodified for the sole purpose of running Programs. Additional licenses for developers and/or publishers are granted in the Supplemental License Terms."
Supplemental License Terms B) License to Distribute Software: "Sun grants you a non-exclusive, non-transferable, limited license without fees to reproduce and distribute the Software, provided that (i) you distribute the Software complete and unmodified (unless otherwise specified in the applicable README file) and only bundled as part of, and for the sole purpose of running, your Programs, (ii) the Programs add significant and primary functionality to the Software, ..."
So not only can you use Java, you can also package it up with your program, although most applications make you download a fresh copy from Sun since its huge.
The Sun source code is a different matter, you need a paid license to use that other than for reference. The license also forbids modifications to the Java code.