When Samuel Finlay Breese Morse (actually a painter) sent the first telegraph message on May 24 1844, there was no special code for the '@' character, though, and it should take 160 years for it to appear.
The Morse Code for '@'
In February 2004, a unique Morse code for '@' was introduced: ·--·-· (Dit-Dah-Dah-Dit-Dah-Dit).
It was the first addition to the alphabet since World War I, prompted by a need to exchange email addresses. There is no code for the exclamation mark, for example.
While Morse code ceased to be the standard for maritime communication in 1999 and is no longer a mandatory requirement for acquiring an amateur radio license (individual countries' governing bodies may still require it), this robust and long-standing form of communication is unlikely to die out soon.
Why Make It Short if a More Roundabout Way Exists
The '@' character in Morse code is a combination of the letters 'A' and 'C', possibly to mimick the look of an '@' (a lower case 'a' inside a 'c').
Unfortunately, this ideographic thinking created a combination that is significantly longer than what ham radio enthusiasts had previously used to transmit email addresses. Before a dedicated code was available, '@' was spelt out as "at", ·- - (Dit-Dah Dah).
The latter "at" is eleven beats long while it takes a full seventeen beats to produce the special '@' code.
(Updated July 2012)