If you have rooted your phone you can delete gmail using a root exploring app, by going to system/app and then deleting the .apk and rebooting the phone. That's how I did it. You can do it so you don't ever sync through gmail too and that stops it sending notifications but you will still receive the emails should you open the gmail app in error.
Not sure of any other ways.
She's up all night 'til the sun,
I'm up all night to get some,
She's up all night for good fun,
I'm up all night to get lucky