It looks like your Switch save data will be locked to your specific console- as of right now, it seems that while there are options included in the system’s settings to allow for data to be moved between multiple consoles, no such options exist yet for save data. Given that cloud backups are not available on Nintendo yet, and that the Switch also lacks the 3DS’s excellent local save backup utility, it seems clear now that there is no way to back up your saves anymore, nor move them between systems.
This is highly opaque and frustrating- and hopefully it is something that is fixed eventually, because what are users who buy a new system supposed to do? What are users whose Switch systems get stolen or broken supposed to do? While accounts and purchase histories transfer over by simply logging in, saves have no such insurance yet.
The Nintendo Switch launches tomorrow worldwide.