Should you report the message text of exceptions?

If you are presenting an error condition to the user, it should probably be a user-friendly message. Exceptions contain technical details that the user should not/does not need to know.

In some situations it could be a security concern to present stacktrace information, so the user should never be shown stack traces.

If you are displaying error messages to the user, there is some point where you consciously make the decision to show a popup, or add a message to a log window. At that point you can translate any exception into a more user friendly message. Note that you might need more information than the default Exception types provide, so you can/should probably create you own Exception types that contain all the information you need to present all the data you need to the user.

No, exceptions shouldn't be shown directly in error messages directly to the user, they're low level technical details and the user almost always wants something more understandable, even if it doesn't provide as much information as a stack trace would!

I say almost always because there are cases (such as in IDEs) where you can consider your users technically competent enough to look at stack traces; indeed in this case they will probably prefer it to a "dumbed down" error message.

However, personally I think stack traces should always be logged somewhere that the user can access so that if they complain that "the program isn't working" you can see exactly what went on if they send you that file.