If you use Google Chrome, you can enable a new Gmail feature that shows desktop notifications for new messages. Go to "Settings", and enable chat notifications and mail notifications to see a small bubble when you get a new message. If you get a lot of messages, it's a good idea to only enable notifications for important messages.
The nice thing is that the notifications are displayed even when you're visiting a different site or the Chrome window is minimized. Gmail's blog mentions an important use case: "you've probably missed an important chat message because you weren't looking at your Gmail window when it came in".
Unfortunately, you'll no longer see the notifications if you close Gmail or Google Chrome, so this isn't a perfect replacement for Gmail Notifier. This issue could be solved by background web apps, a new Chrome feature that allows installed web apps to run in the background.
Right now, desktop notifications are only available in Google Chrome, but this feature has been implemented in WebKit and there's a W3C draft for web notifications. Google Calendar has a similar feature as part of the "Gentle reminders" experiment.