You can change your email preferences in the notifications section of your settings page. You can set your email preferences to to let you know when:
We strive to send emails when they are most applicable to you. For example, if someone you follow retweets your Tweet or someone you mention replies to your Tweet we may send you an email. You will not necessarily receive an email for every retweet, reply, or favorite; for now we will only send you emails when they may be relevant to your activity on Twitter. Note that every email contains a link to unsubscribe from that particular type of notification.
To change your email preferences:
If you're having trouble receiving our emails, please see our troubleshooting section for more information.