What kind of notifications are annoying for you? I think the idea is that they disappear when you switch to the application that emits them, which means they do not stay in the messaging bar for too long.

The current behavior of the close button is actually the result of designer input, see bug 682237.

(In reply to comment #0)
> Instead, I have to summon the application by clicking on the notification to 
> really get rid of the notification.

Note that you can also use right-click->Remove on the summary item.

At the top of my head, some notification that are annoying or sufficient to just see as a notification without a need to switch the application:

- Thunderbird: 3 notification in a row; one telling me the application is launched, one telling me there are new messages, one telling me there are reminders. Talking about an overkill. I know it is launched, I was the one who told it to do so. A notification of the reminder is sufficient for me because, well, that's a reminder.
- GNOME Shell: Calendar reminders pop up. The notification itself is sufficient for me, just like with Thunderbird. Clicking on it gives me the the dialog asking me what to do with them, but the notification remain present even after dismissing the reminders in the dialog. I.e. you'd have to click the notification to get the dialog, then you have to dismiss the reminders, followed by clicking on the notifications again to finally get rid of them.
- Empathy: After connecting to IRC you often get those general messages or login confirmations. I don't even want a notification for those, but the notification itself is sufficient again. No need for me to open the chat first to get rid of the chat window and notifications right away again afterwards.
- Transmission: It pops up with notifications after e.g. a download has finished, but they aren't added to the message tray as separate notifications. Instead the appear when you click on the Transmission icon. You'd first have to go through each notification one by one to be able to open Transmission, because clicking on the notification only dismisses the notification, it does not open Transmission unlike other notifications.
- Accounts: connection error notification. Pressing the X hides them, pressing the notification body gets rid of them without presenting me with an application window. It should really be the other way around.

Some of the issues above should probably be dealt with by the different applications as to when and how they emit notifications, but that does not change the fact that pressing an X resulting in hiding instead of dismissing is unlike I would expect.
About bug 682237, the first comment "It is inconsistent with the behaviour of the close buttons elsewhere". On the contrary! Maybe compared to message tray behaviour, but not to the rest of the UI. Pressing the same icon in the application overview closes an application; pressing X'es in the top-right corner of applications closes them; pressing X'es on tabs closes them.

If there is a distinction between notifications, and the different types of notifications require different behaviour, then the distinction should be made clearer. This goes for the notification itself, as well as the icons used (different icons for different behaviour).

With the exception of resident notifications like Chats and media controls I tend to agree with this report. Perhaps we should reconsider and remove notifications when the x is clicked.

This was changed a while ago.

*** This bug has been marked as a duplicate of bug 687016 ***