Contact-Form-7: 3rd-Party Integration is a WordPress plugin by atlanticbt and zaus that sends Contact Form 7 Submissions to a 3rd-party Service, like a CRM.
Multiple configurable services, custom field mapping. Provides hooks and filters for pre/post processing of results. Allows you to send separate emails, or attach additional results to existing emails. Comes with a couple examples of hooks for common CRMs (listrak, mailchimp, salesforce).
The plugin essentially makes a remote request (POST) to a service URL, passing along remapped form submission values.
Download: http://wordpress.org/extend/plugins/contact-form-7-3rd-party-integration/