A few days ago, I was hit with a flood with emails in my inbox from Twitter saying that someone had mentioned me in a tweet and some which said that my tweet had been marked as a favorite by someone.
Now, I was surprised since the only emails I used to receive prior to this was for direct messages (I have them on to search direct messages on Twitter and archive them). I checked around and saw that it was because Twitter had turned on some new email alerts for me without me explicitly telling them to do it.
If you have been hit with lots of email messages from Twitter recently, you can disable the Twitter email alerts for replies, mentions and favorites by visiting your Twitter profile.
To do that, go to your Twitter profile page and click on the "Edit your profile" link. On the profile page click on the "Notifications" tab. You can also visit this link (https://twitter.com/settings/notifications) directly in your browser.
You can uncheck the boxes next to the notifications you do not require. Once you do that Twitter will stop sending you email alerts. The new email alerts system might be useful for some people, but I feel that Twitter should have kept these options as opt-in rather than opt-out by default.