Is it necessary to verify a user’s email address?

It's pretty much a fact that users hate having to open a new tab, go to their email service, log in, wait for the email to arrive and then click a link/paste a code.

Is it really necessary to do this though? The only reason I ask for an email address is for if the user has forgotten their password. But, my thinking is, it's up to them if they want to run the risk of not being able to reset their password.

Should I verify their email address, or should I just warn them that should they enter an invalid email then they won't be able to reset their password if they ever lose it?