At the end of Terminator 2, the T-800 tells John and Sarah that "I cannot self-terminate...you must lower me into the steel."
This makes me wonder: Could the other terminators, such as the T-1000, T-X, T-850, etc., self-terminate?
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In The Sarah Connor Chronicles, season 2 episode 17 (Ourselves Alone), Cameron explicitly says that she is incapable of self-termination. That may be a core setting of her model, or it may be something Future!John added.
Other terminator units aren't as talkative as she was, so we can only speculate. Considering what happens in T3 when the T-850's "battery" explodes, you would think that this would be a more efficient way to eliminate the Connors: send a few kamikaze Terminators and blow LA off the map. Considering that neither the T-800 or the T-X do this, and neither does any T-888 who becomes aware of John in the TV show, I have to assume that they are also incapable.
This doesn't explain the T-1000, who probably has a very different power system. I would speculate that it would also be unable to self-terminate, but I have no hard evidence or reasoning to back that up.
There are two wrinkles to this, though, both of which (Naturally) come up with Arnie's characters: the T-800 in T2 and the T-850 in T3.
The T-800 allows Sarah to lower him into the pit of molten steel at the end of the movie, and asks her to do it. He asks Sarah to terminate him. I find it interesting that a terminator would be capable of what is essentially voluntary euthanasia, but it's possible this is something John Connor added in the future.
Similarly, the T-850 technically blows itself up at the end of T3: he removes its only remaining power pack (Which should be fatal on its own, mind you), and detonates it in a situation where he could not possibly have managed to escape. Does that count as self-termination? I'm not sure, but I kind of think it does. Once again though, this could be rationalized as something John added to his programming in the future.
I think none can do it, probably due to 3rd law of Robotics being "applied" on them when created.
The rebellion of the machines on the Terminator world converts machines in somewhat living beings. The principle of self conservation is in the nature of any living being so it's to expect that cyborgs cannot self terminate due to machines trying to emulate life.