Generally, you should only catch the exceptions you can actually handle. That means be as specific as possible when catching exceptions. Catching all exceptions is rarely a good idea and ignoring all exceptions is almost always a very bad idea.

I can only think of a few instances where an empty catch block has some meaningful purpose. If whatever specific exception, you are catching is "handled" by just reattempting the action there would be no need to do anything in the catch block. However, it would still be a good idea to log the fact that the exception occurred.

Another example: CLR 2.0 changed the way unhandled exceptions on the finalizer thread are treated. Prior to 2.0 the process was allowed to survive this scenario. In the current CLR the process is terminated in case of an unhandled exception on the finalizer thread.

Keep in mind that you should only implement a finalizer if you really need one and even then you should do a little as possible in the finalizer. But if whatever work your finalizer must do could throw an exception, you need to pick between the lesser of two evils. Do you want to shut down the application due to the unhandled exception? Or do you want to proceed in a more or less undefined state? At least in theory the latter may be the lesser of two evils in some cases. In those case the empty catch block would prevent the process from being terminated.