One in eight people received an offensive e-mail in the last year, government figures have indicated.
Previous studies highlighted concern over bullying emails
The Fraud and Technology Crimes survey by the Home Office also found one in 11 had received similar types of messages by text message or voicemail.
Men aged 26 to 30 were most likely to be the victims of e-mail harassment, the study found.
But women were likely more than men to receive unpleasant messages through mobile phone texts or voicemail.
Almost one in ten women (9.9%) received offending messages via phone, compared with 7.6% of men.
The Home Office study revealed 6.9% of people with a mobile phone had theirs stolen in the previous year.
Carried out in 2002 and 2003, the survey is said to be the first on such a large scale to ask specifically about mobile phone harassment.
It drew on the British Crime Survey (BCS) and the Offending, Crime and Justice Survey.
It also found just over 18% of households with internet access said their computer had been affected by a computer virus over the past year, while 15% of those questioned admitted downloading pirated software or music from the internet.
Just over 2% reported that someone had accessed or hacked into their computer, while 1.9% said they had visited a website on how to commit a crime.
The survey also found just under 1% of those aged 10 to 65 confessed they had knowingly sent a computer virus in the same period.