I had a problem where my iPhone 3G wasn’t notifying me when new email arrived with a sound notification. I made sure the volume on the unit was up and that the Ring/Silent switch on the left side of the unit was set to Ring, but it still didn’t work. I also checked under Settings > Sounds to make sure New Mail was set to On.

This looks like it’s a common issue, and the thing that fixes it most times is performing a hard reset on the iPhone 3G. This worked for me, hope it works for you.