From what I know only Sony new cameras support this. I checked Panasonic and Canon and they DO nOT have this feature. Camera must act both as slave and host via USB ( somethimes this is called USB OTG - "On The Go").
Some Panasonic cameras can connect to a Panasonic DVD burner (but not to a hard drive).
All cameras can be "slave" (connect to a PC) but very few are "host" also (connect to a regular "mass storage device" like an external hard drive, SSD drive or USB stick. Sony calls this feature "Direct copy" not OTG ( maybe because does not support allthe features required by USB OTG).
I think for most this feature is usefull not for long home recordings but if you travel.If I travel for 2 weeks, I may fill all 64 GB and an additional card in a few days time, but I can download all the stuff on the external drive if needed and delete the internal flash. As long as you keep the file structure intact the camera can even play later the content from the drive, but anyway most will do some editing and remastering of the content as AVCHD or Blu-ray disks anyway.