Informing Healthcare, a Welsh Assembly government programme, is testing My Health Online, which would also enable all patients to book GP appointments without picking up the phone.
Further along they may want to look at their own medical records on their home or work computer to help them find out more about their health.
Patients will be able carry out these and similar health-related tasks and see their information through a secure web site we're developing, called My Health Online, which is now being tested at a number of GP practices.
It's all part of the plan to give each patient in Wales an electronic individual health record. This will bring together the information held about each patient, wherever they have received treatment, and supports the Welsh Assembly's vision for people to be more actively involved with their own care.
The cutting-edge technology is being piloted at four GP surgeries in Anglesey, Ceredigion, Swansea and Bridgend, as the IT revolution gathers pace in NHS Wales.
If the pilot projects prove successful, a business case will be drawn up and the scheme will be expanded across Wales.
Patients will find benefits of using My Health Online will include:
Finding information they would otherwise have to ask for for example their immunisation history
Helping understand the history of a particular condition
Improving awareness of a condition
The development comes as individual health records are being rolled out to a number of GP out-of-hours services in Wales and emergency hospital staff have been given access to a limited patients' health record in Newport.
Dr Martin Murphy, clinical director of Informing Healthcare, said: "My Health Online will mean that people can access health services, such as making an appointment or ordering a repeat prescription at a time that is convenient to them.
"It will mean that someone doesn't have to pick up the telephone."
And a Welsh Assembly Government spokesman said: "My Health Online offers the opportunity for people to book appointments or order repeat prescriptions online rather than calling or visiting the surgery. This is simpler and more convenient for patients."
The technology could also be expanded to allow patients with chronic conditions to keep an online diary or health log of their symptoms by the side of their medical notes.
Such a move could help to improve the treatment they receive from their GP, by increasing a professional's understanding of their condition.
About 60 patients at Meddygfa Star Surgery, Anglesey, have tested the ability to order repeat prescriptions online - each has been given a unique and specific password to access the online facility through the practice's website.
Some of these patients will then be able to collect their medicines directly from the rural practice, which dispenses for about two thirds of its patients.
The other repeat prescriptions ordered online are automatically passed on to a patient's pharmacy where they can then collect their drugs.
Maggie Alcock, the practice manager, said: "Repeat online prescriptions has worked very well - it frees up telephone time for staff who can deal with the requests whenever they have a quiet moment.
"The feedback we have had suggests that it is definitely a benefit."
A smaller group of the practice's patients has been allowed read-only access to their medical records online.
Ms Alcock said some of the patients had experienced problems accessing the information and there have been some general concerns about the security of the data.
But she said those who had accessed their records found it helpful, especially when filling out insurance-based forms.
"All of our information is kept on computer and I think this electronic transmission of data is the way forward, although there are still some issues about security," Ms Alcock added.