These are "largely preventable patient safety incidents" that should not happen if proper measures are in place.
There were 60 of these incidents in Wales' seven health boards from April 2012 to present.
The Welsh Government said: "Patient safety in Wales is paramount."
Items mistakenly left inside patients following surgery or procedures include vaginal swabs, a surgical blade and a silicone object.
Wrong site surgeries included the wrong joint being injected, the wrong side pleural biopsy, operating on the wrong spinal disc and the incorrect tooth being removed.
Incorrect implants or prosthesis included a hip replacement, a lens and a pacemaker.
One person was also able to fall from a window which was within reach of patients at floor level and could be opened without the use of a tool.
A Welsh Government spokesman said: "Every year, hundreds of thousands of people receive high-quality, safe care in the Welsh NHS.
"However, in an increasingly complicated and modern healthcare system, problems can unfortunately happen.
"When problems do occur, NHS staff are encouraged to report all incidents so they can be investigated openly to promote learning and provide open feedback to patients and their families as part of our commitment to an open safety culture."
Between 2012 and 2016, Abertawe Bro Morgannwg health board had 15 "never events", Aneurin Bevan had eight, Betsi Cadwaladr had 15, Cardiff & Vale had 13, Hywel Dda had four and Cwm Taf had five. There were none in Powys.
NHS Wales publishes an annual list online of all the mistakes made.
Abertawe Bro Morgannwg
Aneurin Bevan
Betsi Cadwaladr
Cardiff & Vale
Cwm Taf
Hywel Dda
A silicone object left inside someone, a patient falling from a window and the wrong person undergoing an exploratory procedure are among "never events" which have happened in Welsh hospitals.