Q:
Email Verification
You can make Anet or the game to “remember” the network, then you should only be asked if a new IP range gets into play.
BTW most players have dynamic IP, so most of them change IPs every day.
It is possible to remove the authentification, but it is not advisable. You have to write a support ticket to get it done.
ArenaNet Communications Manager
If you’re asked to verify every time you log in, that’s very odd. Even with a dynamic IP, you should have a range of “whitelisted” IPs that prevents you getting the request for verification each log-in. I suggests contact Support by filing a ticket through the “Ask a Question” tab on that linked page. They can help you figure out what’s going on, or they can help you remove authentication, as you desire.
For tips on what information to provide in a ticket, please read this post.
Communications Manager
Guild & Fansite Relations; In-Game Events
ArenaNet