yes, there is some automated programs, and servers can self save and delete old file that they don't need and the technology is improving all the time so soon there will be computers that can even turn itself on and control itself.
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Yes. Computers are used in all sorts of equipment that need to operate without human intervention. Unless you include switching them on.
Domestic appliances like Washing machines, bread makers, TV's, DVD's, dish washers etc. all use digital computers in them. All work and follow complex instructions and take inputs from their own workings, without constant attention.
No. Not until computers become self-aware and start re-writing their own software without the need for human intervention.