Although all other answers are technically correct, I would recommend you adding the custom path to the beginning of your PATH, not at the end. That way it would be the first place to look for instead of the last:
Add to bottom of ~/.bash_profile
:
export PATH="/cygdrive/C/Program Files/Java/jdk1.6.0_23/bin/":$PATH
That way if you have more than one java
or javac
it will use the one you provided first.