The Nintendo Switch will feature additional storage via SD cards but will not allow for any external USB hard drives to keep the console portable.
A report from Lets Play Videogames states that the current development hardware for the Switch allows SDXC cards up to 128GB to be inserted into the tablet portion of the machine. Apparently the development model does allow software to run directly from the SD card.
The Switch model in the trailer apparently had the SD card slot located underneath the kickstand on the back of the tablet.
Lets Play Videogames also reported that Nintendo will not allow for external USB hard drives to be used with the Switch. While this at first seems like a strange decision that could potentially limit Switch's storage options, the company's reasoning seems to make sense. The report states that Nintendo thinks external hard drives would limit portability, as people would have to transfer games from the hard drive to the tablet in order to play on the go. This of course would be a massive inconvenience and would probably cause people to only play when docked.
A final report from the site also suggests that the Switch model used in the reveal trailer featured a USB C port on the tablet for charging when away from the dock. This was positioned on the bottom of the device, meaning if the design sticks for the retail model you will not be able to charge it while using the kickstand.