People will do anything for God. And if they become convinced that a person speaks for God, they'll do anything for that person. Think about people that shoot abortion doctors, suicide bombers, jihadists.
As far as giving up stuff, people feel good about giving things up for God. It's a sacrifice.
So why would anyone think JW's speak for God? Honestly, they have one hell of a sales pitch. Like Dan mentioned, they immediately hang the "live through armageddon" threat in front of you, then tell you about the paradise you can choose instead. And finally, polish it off by telling you what you need to do. Classic sales -- invent a need/fear, then show how to get it/avoid it. (Who knew we needed "anti-bacterial" soap before they started selling it to us?)
It's not that people that become JW's are idiots, they are just tricked. It doesn't take much, especially if you already have some built-in assumptions. For instance, if you believe the Bible is the inerrant word of God, all they have to do is show you a scripture that disproves your current Church's doctrine, proves their own, and warns you about spending any more time in that Church. Once you see it in your own copy of the Bible, they have a hook in you. The hope is that you won't go back to your church to verify their claims. They hope you'll take their word for it. (They aren't malicious in this, they think it's for your own good) If you do take their word, that's another hook. Pretty soon they tell you about the "Faithful and Discreet Slave", a class of humans allegedly headed by the Governing Body of men in Brooklyn. These men -- while imperfect and fallible -- speak for God. Whatever they say, goes. If you stay on the hook past this one last belief, they have you.
Most people never get that far. But for the few they manage to trick into joining, it's very powerful. How can you really ever see the falsehood in an organization that you believe DEFINES truth?