How can I control wi-fi data use? I'll be taking a vacation next summer, and on the cruise data use is sold per megabyte. If I JUST want to check e-mail on my android device, how the heck do I do that? How do I prevent all the other apps on my phone from accessing the wi-fi (cellular will be turned off, or I'll be using my wi-fi only tablet). 

My objective is to limit network use to just the one or two apps that I really want to see results from. I can't seem to find anything in the settings that would allow me to do this.

Is there any way? I'm probably willing to root my tablet if necessary.

Devices available are the moment are a Droid 4 phone, and an Acer Iconia A200 tablet.
Go to settings, accounts and disable Sync. It will reduce your data consumption by a lot.

You still can check for emails manually though when sync is off. Remember this is the only way to get fresh mails then :)