Contrary to popular belief, inmates can and do email. This is not to say they all have access to the Internet but they all do have access to email.
JPay, a popular money sending service for inmates, has an email function. They also offer a video chat service. Not all prisons allow this service. I have personally used this service for correspondence with Kelly Gissendaner and money transactions for Tiffany Cole.
Emailing A Prisoner is another email site. This one sends pics as well which most do not. I have not tried this site but there are a lot of features that look pretty convenient. They hide your address if your uncertain about the inmate and the entire service costs only $1.00.
CorrLinks is an emailing service set up by the Bureau of Prisons. The tax payers don't pay a thing for this but instead, the ginormous extra funds that inmates pay for commissary (think $2.50 for a honey bun)goes toward the cost of this service.
Most county jails do not have this service. You may find one or two with some type of email service enabled so go ahead and ask the Sheriffs department just to see. The SanDiego County Sheriffs Depart, for instance does offer email services to the family of inmates.
Federal inmates were the first to gain this privilege with the hopes that allowing more correspondence and closer contact with family and friends will serve as a aid to reduce recidivism as well as make prisoners happier and more complacent.