Registration w/out sending password

I’d like my users to specify passwords in registration form, because on my host unfortunately mail() function is disabled and no one will ever get mail 🙁 (I just setting up site, so it’s not big problem now, but after launch…). So how to add fields for specifying password to register form (and since my site utilizes also bbPress for bbpress register also) and replace sending password in mail by e.g. reCaptcha (for spam protection)?