More than 3,500 complaints were made to the Office of the Ombudsman about public bodies last year, a rise of 3%.
This follows on from a rise of 11% in 2014.
The most complaints were about the civil service, with 1,397 complaints or 38%, followed by local authorities and the Health Service Executive.
In his annual report for 2015, Ombudsman Peter Tyndall, however, noted the low level of complaints his office receives about hospitals.
Mr Tyndall said an investigation discovered that some people are afraid to complain because of the possible consequences for their treatment, or because they believed it would not make a difference.
He has made 36 recommendations to improve the hospital complaints system for patients but while the HSE accepted these, Mr Tyndall has expressed concerns about the delay in acting on them.
"In most cases the delivery of public services goes well. However, if people don't complain when things go wrong then people will experience the same problems over and over again," Mr Tyndall said in a statement.
"When people complain it gives service providers an opportunity to put things right and to stop the same mistakes happening again."
However, Mr Tyndall has said he is concerned that people are not entitled to complain about clinical judgment issues.
Speaking on RTÉ’s News at One, Mr Tyndall said it can be a matter of patient safety and people should be entitled to refer such concerns to his office for consideration.
Mr Tyndall said he is waiting to hear from Minister for Health Simon Harris in relation to legislating on the issue.
He also said it is "worrying" that people are afraid in some cases to complain about the HSE and it is really important to complain to ensure changes can happen.
Private nursing homes came under the Ombudsman's jurisdiction for the first time last year but Mr Tyndall said so far the number of complaints has been low.
Among the other complaints dealt with by the Office concerned the State Examination Commission, welfare payments by the Department of Social Protection and dog fines issued by county councils.
Housing has also become a significant issue for the Ombudsman's Office.
In one case, the Ombudsman investigated the case of a woman with two children who was on Kildare County Council's social housing waiting list for ten years.
After raising the case with the council, the family were allocated a home through a voluntary housing association.