Depends,on the species of tortoise.
@Tom will be able to answer this better then me on some species. Others, not sure who, will have to fill in for species Tom can't.
There are many species which need a high humidity especially the species which live in tropical regions.
For example Kinixys homeana and kinixys erosa need a very high humidity because they live in the rainforest of westafrica. C. carbonaria and denticulata need also a high humidity but they could also accept lower humidities because they live in the rainforest and in the grassland where the humidity isn't so high. So all in all you can say that species which live in rainforest or in region which have a tropical climate need a higher humidity. For some species which can live with a very high and a "higher" humidity is its important to know from which region they come. Hopefully that help a little bit it's every time difficult for me to explain things like that in English..
It has never been a problem for me, in my enclosures with the way I do things. I can't say I have ever seen anyone else have a problem either as long as temps didn't drop too low.
I just raised 20 of them that way, and they are all fine and dandy.
Good to know. So at this point I'm feeling high humidity wouldn't really be a problem unless temps drop low. So in a way there's no such thing as TOO high of humidity as long as temps are right.
I am by far not an expert but based off my own experimenting, higher humidity has helped with shell growth. All of my Russians were at some point wild caught. When I got them they each had very rough and bumpy shells. After keeping my humidity between 60 and 70, they have all smoothed out and seem to have a natural shine. Just my own experience with my Russians.