or would it be more useful for conductors in some other space? generators/turbines?
For one, it would allow current-based forms of memory storage. Right now, non-volatile memory is always stored as a voltage*, because static charges can be held without decay. Superconductors allow that for current. This also is great for sensors. For example whereas a copper ring will have a brief current when exposed to a changing magnetic field, a superconductor will have a current that perfectly tracks and cancels any magnetic flux it is exposed to. It can bring AC effects down to DC. And due to zero losses (and zero Nyquist noise), it could be used to, for example, make more sensitive antennas.
Secondly, even if you don't care about the losses in terms of power consumption, you almost always care about losses in terms of heat. Superconductive motor windings, for example, would allow motors to not only be more efficient, they could also be much more power-dense because of less heat generation.
And then there are the really fun applications, like levitation.
* (Or eg. a ferromagnet)
It's almost impossible for one person to list all of the ways technology would change, and the world with it.
It would be awesome. Off the top of my head:
Big electromagnets would use it: MRI machines, magnetic plasma machines (fusion reactors), industrial magnets (for lifting), etc. A lot of the size and complexity of some MRI machines is the cooling system for the magnets — this would be unnecessary.
There are designs for superconducting transformers that could be smaller and more efficient than current transformers.
Long distance power transmission would be considerably cheaper at high power levels.
I can imagine that some interesting motor and generator designs would become possible.
Superconductors enable some deep magnetic magic which is used in all kinds of things from fusion reactors to MRI machines.
Current superconductors require cryogenic temperatures to operate though, which limits their applications, makes them extremely expensive to operate, and too complicated for large scale manufacturing.
An ambient temperature superconductor, even if the material itself was hideously expensive, would make these extraordinarily powerful technologies much easier to develop and deploy.
From The Electrochemical Society [1]: "More exciting is the prospect of finding materials in which superconductivity occurs at higher, more usable temperatures. If long-distance power lines could be made of superconducting materials, for example, electric bills would plummet."
So until I can bench test it or someone whose reputation I trust has bench tested it for me it doesn't exist.