How can I receive a new verification email?

There is a page to request resending of your activation code which can be found here:

https://club.pokemon.com/us/pokemon-trainer-club/activated

If you are unsure of your username you can try this link:

https://club.pokemon.com/us/pokemon-trainer-club/forgot-username

There doesn't seem to be much that can help you if you have forgotten what email address you used. I would imagine few people have so many email addresses that they can't just check all accounts.

To help to locate emails from them the address used to send the emails is noreply@pokemon.com so you can try searching all your email accounts for emails from them.

Also as extra information I quote the text you get after registering:

Thank you for creating a Pokémon Trainer Club account. We have sent you an email to verify your account. When you verify your account, you'll get 25 Trainer Tokens as a reward! You have two days to use your Pokémon Trainer Club account without verifying your account. After that time, you'll have to verify your account before you can sign in again.

So next time when something tells you that you need to verify do it immediately! :)

As a final note if you are having problems because you put the wrong email address in or something similar to that then their web page suggests:

Pokémon Trainer Club Account Setup and Log-In Problems:

If you are having trouble with account creation, or are having issues logging into your account, you can email us directly at: techhelp@pokemon.com.