A bronze bust statue of Norwegian polar explorer Roald Amundsen at Canterbury Museum is an example of what can happen from cumulative touching.
Amundsen had a large protruding nose which was captured in the bust, but touching over the years has made it shiny and bright.
"We have quite a light touch when it comes to touching," deputy director Jennifer Storer told the Herald.
"There's kind of been this right of passage which everybody does, they rub Roald Amundsen's nose, which is quite prominent, I should say.
"He was the Norwegian explorer who discovered the South Pole - you will see he's got a quite bright, shiny nose."
Canterbury Museum had a scare when a child got their finger stuck in a multi-million dollar meteorite and couldn't get it out.
"So, a 49,000-year-old meteorite weighing almost half a tonne and the kid put his finger in and got his finger stuck," Storer said.
"Meteorites are incredibly dense, if we had to cut his finger out, we didn't know of anything that would be able to cut the meteorite."
Luckily, oil was able to be used as a lubricant and the child was able to wriggle his finger free following the brief scare.
Auckland Art Gallery said most of their artefacts were not for touching and most of their visitors understood and complied with the rule.
"Most of our visitors respect and treasure the taonga of the gallery as much as we do," spokeswoman Samantha McKegg said.
"The painting Still on Top c.1874 by James Tissot (1836–1902) was damaged when it was stolen from the gallery in 1998.
"This painting ... was extensively damaged during theft, suffering tears and losses. It took two years for a team of two conservators to complete the restoration treatment."