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:
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.