I complete agree with you Blaine about not throwing away information. Keep everything, and add to that information whenever you have something to add. For example, when a caller catches an exception, the caller always has some indisputable and unique information it can add: exactly what it was trying to attempt when the failure happened.
Dropping this information is like using a shredder. It's not responsible behaviour for developers to shred information that might be useful to the poor sod who had to fix your buggy code at 4am in a production environment.
Actually, such information is often the 'single golden clue' that leads to a rapid diagnosis of the error. For this reason, I believe it's justified to add such information even when unchecked exceptions occur. "Yes, you got a NullPointerException, but what exactly were you trying to do when you caught the NullPointerException?"
For that reason only, I disagree with you about catching only the most specific exception- I always catch, wrap and rethrow any subclass of java.lang.Exception. I started handling exceptions in Java this way back in 1997, and haven't seen anything since that has caused me to change my mind (but I'm open to debate).
What a great idea! I love it. I agree if you are checking for generic exceptions and then wrapping them into more domain specific for more information, then rock on. My original comment was aimed at catching generic exceptions in your code and then doing nothing with them. I still generally try to catch the things that I expect to go wrong and use my top level to catch things I didn't. Always adding more information is a good idea in my opinion especially if it gives you more context. As with any rules, it really requires thought and good judgement to make a good program right? Thanks for the suggestion!