The office of the Ombudsman dealt with 3,412 complaints in 2012, a slight decrease on the previous year.
The highest number of complaints involved the Department of Social Protection, with 624.
The office also received 413 complaints about the Health Service Executive.
There were nearly 600 complaints against local authorities around the country. The office dealt with a total of 11,000 inquiries last year.
The figures are contained in the Ombudsman’s 2012 Annual Report.
It is the last report from Ombudsman Emily O'Reilly, who will take up the position of European Ombudsman on 1 October.
Ms O'Reilly said she had mixed relations with public bodies over the year.
She accused the Department of Health of "running to lawyers" when high-stake cases were involved.
The Ombudsman also said she was disappointed and faced ethical dilemmas when findings made by her office resulted in welfare schemes being cut or suspended, as happened with the mobility allowance and motor transport grant schemes after she found them to be operating illegally.
She said, however, she had to make her findings and the Government makes policy.
In relation to discretionary medical cards, Ms O’Reilly said that Fianna Fáil leader Micheál Martin is not wrong when he says people are being denied things they would have been entitled to in the past.
She said the letter of the law is been applied when it comes to the likes of the discretionary card and that authorities are not looking at people's particular circumstances when they apply.
Equally, she said that Taoiseach Enda Kenny is not wrong in his statistics in relation to medical cards and benefits from the HSE.