Is it possible to create gmail, facebook and twitter account through API?
Short answer: No.
Well for Google Apps you can sync a user directory (via LDAP) using Google Apps Directory Sync. This will provision, modify and de-provision any number of accounts without CAPTCHA verification. You will be billed for each one you create and they will all be in a domain you must own so there are practical limits for abuse, but this scales out to tens of thousands of accounts. There is no method to do this for Twitter and Facebook but things like this are a large part of the draw (for companies) of services like Yammer and App.net.
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