On Twitter, how can I receive an automatic notification through email if somebody writes an @-message to me?
A couple of options:
Follow the (private authenticated) RSS feed of your @replies/mentions: http://twitter.com/statuses/replies.rss - since its authenticated it will require you to sign in and won't work in Google Reader (unless you use Yahoo Pipes as an intermediary)
Use a web-based service (such as http://pu.ly) to monitor your mentions and email you when they appear
Mention Notifier is a free service that should do the job:
Twitter now supports email notifications for mentions as well others.
Check your settings to see if this feature was rolled out to you.
Here's an article that describes the process. Essentially you can use Yahoo Pipes to find replies or mentions within an RSS feed, then provide that feed to the FeedMyInbox service.
I have multiple accounts. I created a search for @name1 OR @name2 OR @name3 and then I subscribe to this by RSS (search, then look for the subscribe to this query button on the side of the page).
The search for @name solution does not require authentication and works in google reader.
I use the same technique to create a merged @mention column in TweetDeck because having a few mention columns will use up the whole screen.
If your name is reasonably unique, leave of the @ to capture messages from people who don't get the @ convention yet.