When should a website require e-mail validation for user registration?

I am developing a website where users register with their basic information including e-mail address. My question is, should I register users directly or send them an email with a link for verification to use their accounts?

I think it depends of the type of the website, if it is about some "serios" thing like e-commerce, it should require activation but if it's a simple thing (like a forum) then it might not be necessary. But I am not sure.

In the terms of security, if a user validates their email address, I can assume that he's not a bot and is a real person. But I can use a captcha on the registration screen to avoid this kind of check (actually I need to use captcha anyway).

So, not requiring email validation has the advantage of simplifying and quickening the registration process (which is related to the overall user experience), on the other hand, it has the disadvantage of not knowing if the e-mail belongs to the user or not. So it seems like a trade-off. How should I decide?