My rule of thumb with both my children has been "if he/she can do it him/herself, he/she should". That includes going to the toilet, washing hands, etc. My four-year-old boy goes to the toilet by himself, whether it be in restaurants, shopping malls, etc. or at home. My seven-year-old obviously goes by herself as well, and has since she was about four (when she could reach the faucet without being lifted).
I've found this approach helps their self-confidence and their autonomy. While that means that sometimes, in the morning, they decide to make breakfast (and make an enormous mess) before we even have a chance to get up, it also means there's a lot of things we don't need to do anymore (like putting their clothes on in the morning) - and they're often proud of their accomplishments because they know we value autonomy.
Adolescence is definitely too late to stop accompanying them, diapers is definitely too early. If you ask them "did you wash your hands" with some of their peers present and they're embarrassed, it may be time to let them take care of their visits to the little men's/woman's room themselves...