it will depend on some things.
i try to keep my hands free. I will probably have a camera in one and if im thirsty i may carry a disposable water bottle in the other until its gone. I try to use public water fountains when possible, keeps the carrying to a minimum.
i have Point N Shoot cameras so i can put them in my pockets when not in use.
as far as maps, i usually have a paper one so that isnt an issue.
as far as buying souvenirs, i do that but i know what i will buy so that i either buy it on my way out so i dont have to lug it around or i have my "buying" day(s) or will buy it when im going back to the lodging. Either way, im not carrying stuff all day, but at the most half of it.