I can send an email to you asking for information, and then push it from my mind until I get a notification saying that you've responded. Without notifications I'd have to go and check repeatedly to find out if you'd got back to me yet.
The important thing is to keep important notifications and unimportant ones separate, so that you're only notified of things you actually care about.
Sometimes, a person doesn't want any notifications at all—for example, when they're working and "in the zone," or watching a movie, or playing a game.
Sometimes, you want to be notified about pretty much everything.
The decision about when to be notified or not, and what's important vs. unimportant, should be your decision, not your computer's.
But isn't that the status quo?
I can't think of any piece of software I use that doesn't give me a fairly easy way to temporarily turn off the notifications. I don't want to get notified by Facebook? No problem, I shut it down. Don't want to be interrupted by my telephone? I put it in silent mode. Etc., etc.
The OSX dock bounces when an application thinks it has something important to tell you. Windows grab focus away from the user when a process completes. MS Outlook throws email notifications up at you, even when you're presenting to an audience on a large screen—always fun to see the subject lines of emails showing up while a presenter is trying to talk.
On your iPhone, you are forced to dig into the preferences to find and turn off the "Automatically ask to join networks" option if you don't want wi-fi notifications popping up all over the place any time you are on the move.
Off should be the default for notifications, not on.
Maybe I'm biased, though; exploring the Settings/Options is usually the first thing I do when I run a new application.
But damn if it doesn't grab the focus of my screen while it's there. There are a lot of times I'm looking at a piece of paper while typing an email or report, not looking at the screen. If I've gotten a new email since I started typing, everything I typed in the meantime has been triggering shortcuts on the email notification. Some of them have been deleted because I was typing when it popped up, some people have gotten part of my typing as an email response.
Lack of attention on my part? Sure. Lack of foresight on Novell's part? You bet your ass.
But notifications in moderation are fantastic.
But, when I'm on call, I know that if anything is important enough that I have to respond to it RIGHT NOW, I'll get paged. And that lets me completely forget about checking any other form of electronic communication until I feel like it -- which, on the weekend, can be a day or more.