The major exception for me is em-dashes, which I use all the time.
There are also a few punctuation marks on a standard keyboard that don't get used very much outside of programming and other specialized contexts. {}\|
Another interesting thing related to punctuation is that the use of some punctation is really overloaded. Quotation marks in particular can mean literally quoting someone, a scare quote, an indication that something is a term of art, titles of certain types of works, and probably some other variants.