Does anyone use an application system to accept members to your site?
 

and if you do, can you link me to the appropriate mod or add-on?

As it is right now, I have to have people email me for an application, which they fill out and email back to me. I want them to be able to go to the homepage and just fill out an app, post it to me, and wait for a reply before they can register. Any ideas?

Try creating required profile fields and making all new members moderated.

That way you'd have to approve or disapprove them.

If you disapprove them, just e-mail them why (if you want) and delete the account (so you don't have a ton of denied accounts)