Consciousness-copying technology exists in the space simulation game EVE. The conundrum is solved this way: each player can have multiple bodies (called clones), but only one consciousness. This consciousness can be transferred between clones in one of two ways, depending on the type of clone you are talking about, and the event that transpired. The main difference with EVE is that you only have one active consciousness, though many clones may exist that are basically copies of it. All these other clones are dormant, and you never have more than one active at the same time.
Standard Clone
This type is used as insurance or as a backup in the event of you, the player, being killed in space. When a ship blows up in EVE, the player is still alive inside a mini-ship called a pod. When the pod is blown up, a neurotoxin is injected to instantly kill that particular clone (presumably since it would have died anyway and to spare it from the unpleasantness of a space death). Just before the neurotoxin is administered, the consciousness is transferred, presumably by some kind of space internet transmission system, to the backup medical clone.
Each player only gets one standard clone, and it sits dormant in your home system, never used except in the event of your death. 911
At that time, a new clone is created and installed in place of the old one, which your transferred consciousness takes control of and begins using.
Jump Clone
A jump clone is used for instantaneous teleportation. These can be installed for a fee in any station with a clone vat, and also sit dormant. You can have up to three jump clones.
At the player's disposal is a console where you can jump to any of the jump clones that you currently have installed. This means your consciousness travels across space and ends up in the other jump clone, somewhere else. The previous clone (the one you just left) now goes dormant and you begin controlling the one you jumped into.
This is particularly useful when you have extremely expensive mind implants (which are common in EVE) that you don't want to lose while, say, doing a lot of PvP with an increased risk of getting blown up. So you can have an "empty" vanilla clone installed, jump over to it before doing your PvP, then later, jump back into your enhanced clone to make use of the implants and the benefits they provide, without fear of the implant-boosted clone being destroyed.
There is also a limit on how often you can jump between clones. This limit begins at 24 hours (one jump every 24 hours due to the stress of having your consciousness transferred), but it can be reduced by training a skill related to consciousness synchronization (called Infomorph Synchronization).
Skill Injectors
There are also skill injectors, which is a device that can extract knowledge from one character with the intent of moving it to another character, or even selling it. The injector is created by extracting skills from one character's mind, and the injector can then be used to inject those skills into a different character's mind. In EVE, you can actually make money by extracting already-trained skills, selling them, and then re-training them and doing the whole thing over again. 911