Separating body and mind is something generally unachievable in reality, so it makes excellent gaming fodder. There are several different means of achieving it in a fictional setting:

• Spiritual: There is a conscious spirit inhabiting your body, which can leave the body and travel around independently, or perhaps even inhabit another body.
• Magical: Magic might be able to manipulate consciousness by transferring it to a different body, or to a temporary storage container, such as a Magic Jar spell in Dungeons & Dragons. Some beings may have an innate magical ability to do this.
• Technomagical: Magic with the trappings of technology. Someone invents a machine that can transfer souls or switch minds between people, with little more than a hand-waving technobabble explanation.
• Physical: Like Yoda's midi-chlorians here, or the trill Dax in Star Trek: Deep Space Nine - consciousness resides in one relatively small physical part of a body, while the motive part is largely a vessel that can be inhabited, and changed if necessary. This can be relatively benign as in these examples, or it can be played as horror, with hostile parasites that infect and take over control of a body's personality.
• Medical: Brain transplants can be performed successfully, and transfer a living brain from one body into a donor body. Perhaps a living brain can be stored in a jar, without a body, and be wired into a computer system so it can communicate and send control signals to robotic servants.
• Computational: A sophisticated enough computer can replicate the synapses of a brain, and run a full simulation uploaded from someone's brain. This is a copy of the original consciousness, but philosophically some may consider it a continuation of the same consciousness, because it will possess all the original's memories and personality - especially if the original organic brain has to be destroyed to upload its memory patterns. The computer copy may run in a fixed computer system, or could be loaded into either a robotic or organic body, giving it mobility. See Ghost in the Shell or Steve Jackson Games' Transhuman Space roleplaying game.

Transcript

Luke: So, if you're Yoda's clone, are your midi-chlorians in there?
Kermit: Kind of a personal question, that is, hmmm?
Luke: I need Yoda's midi-chlorians for a quest.
Kermit: Merged, our personalities have. Commissioned this new body I did.
Luke: But... you Force Transcended!
Kermit: Right.
Luke: Huh. I guess that's why you were so blasé about it. But... why?
Kermit: Pass up the opportunity to be a dashing young tadpole again, would you?
{beat}
Luke: I'll stick with just being me.