I don't receive Gmail notifications on my phone recently, no sound, no light and nothing appears on the notification bar. Searching the web, I figured it might have happened because I turned syncing options off. So I turned it on except for some syncing options such as Pictures and browser. I still am not getting notified of new emails. What's wrong?
Summing up results from the in-comment-discussion:
Starting with Android 4.1, notifications can be disabled on a per-app basis: Either by long-pressing a specific notification in the notification area, and navigating from there to the app which sent it -- or directly from the Android settings in Apps → Manage Apps, and selecting the app you want to disable notifications for: here you will find the possibility to allow/forbid an app to place notifications in the notification area. This is valid generally and for all apps, starting with Android 4.1.
As with the Gmail app, some apps also offer this option themselves (which then also works for Android versions prior to 4.1). You find it from inside the app, when visiting its settings page(s). But as said, this will vary between apps -- not all apps offer this option.