In general spacecraft are supplied with propulsion systems often with substantial redundancy in the plumbing and engines or thrusters so they can dependably and reliably perform orbital maneuvers in space. The emphasis is on the word perform. They wait for commands from Earth before doing anything with it. You could say that spacecraft are carefully micro-managed.
For deep space missions, this is done with an abundance of caution to protect the substantial investment of time, people, and resources and the science to be gained. For Earth orbit, in addition to protecting all of those (with commercial gain replacing the scientific gain in most cases) there is the additional responsibility of not interfering with all of the other satellites in orbit.
I was surprised that even the very expensive James Web Space Telescope does not seem to have the ability stay put by itself as hypothesized in this answer, and without constant station-keeping instructions successfully received from Earth, would just drift away from it's libration point orbit.
To contrast, planetary explorers (as opposed to spacecraft) such as rovers and in the future flyers and/or hoppers execute sequences of tasks in rapid succession that require first-hand knowledge of the local environment which makes it beneficial to operate semi-autonomously. For example, based on experience from a number of past and present rovers on Mars, the Curiosity rover on Mars is capable of keeping itself busy for a day or so both in movement and sample taking and analyzing samples as described in this answer, and the EXOMars rover will potentially have a degree of autonomy as well.
So my question is, What are the future prospects for spacecraft autonomy?