Should my app send a confirmation email on user registration?

I'm grappling with the user registration experience for my application.

I'm considering this model:

  1. User enters...

    • Username
    • Password
    • Password confirmation
    • Email address

  2. The app displays a message saying "Please check your email to complete your registration" and sends them an email sort of like...

    Hi username.

    It appears that you would like to register for Useful Web Application.

    If so, please click this link to complete your registration:

    http://usefulwebapplication.com/reg_confirm/bxl46ehfe

  3. They click the link and it takes them to a page saying, "Thanks. You're registered."

But I'm wondering if that second step is necessary.

I've noticed that Instapaper just registers you and logs you right in with no confirmation email.

Should I skip confirmation emails?

The main reason I want users' emails is so I can send a "reset password" link if they forget their login info.

(In case it's relevant, this app isn't a forum or a social site. It's more of a software as a service utility type of thing.)

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