You don't have to disable data access to turn off any application. That way, the inconveniences of having no data access far outweigh the supposed irritations the said app will be causing you in my opinion.
For those using Android phones its easy. Just go into Settings-->Applications. From here you have two options; 1. Choose Manage Applications, & you will be presented with about for tabs. Under any of these(esp the Downloaded or Running tabs, scroll down looking for the whatsapp app, tap it once & you are given options to either Force Stop, Uninstall, or Clear Data. Choose Force Stop, & confirm when asked. 2. If you choose Running Services the process is the same, look for whatsapp and force it to stop. If you wish to restart it just open the whatspp application and it'll start running again. Another way is just download a task killer from the Play Store, and use this to stop any application you wish, not just whatsapp.
This way you can continue using your phone normally without whatsapp annoying you. Disabling your data is not the best because what happens when you want to check your mail or surf the net? All those pending messages will come through and if you are trying to avoid someone they'll know you are back online. I don't wish to shoot down a suggestion made by someone but I thought the above solution could cause more issues than the one being solved. I don't know how to do it on an iPhone as I never owned one but I'd imagine the principle is the same. I also want to think iPhones come with built in task killers, any decent phone should allow you the option to stop any program without shutting another service down. Anyway, I wouldn't be surprised if there was no way to turn it off on an iPhone as its a rubbish phone; it doesn't give you the freedom to do what you want, install what you want, copy numbers or remove battery, can only download stuff from their store, etc. Its locked down like a landline that I ask myself what the point is. The only way to go round this is to jailbreak it, but why should it come to that for such an expensive gadget? I appreciate this thread is not about bashing the iPhone so I'll stop.