Just a bit of follow-up research on this subject.
A quick check of the Android phones on
GSMarena.com yields about 37 phones that claim they're USB-host-compatible. Still, as others (and I believe you also) have pointed out, that doesn't always mean anything since, technically, USB host has been integral to Android since about version 3.1 and it was also back-engineered into some early Android releases on certain phone models. It's really not just a matter of what's provided for in the Android operating system, but whether the hardware on the device supports the functionality and whether the vendor/manufacturer has enabled the functionality. And this typically requires the acquisition of a USB OTG cable to use the functionality, but these are quite cheap (if, of course, you can find one that fits your phone).
So, if you've got a phone and you want to know whether it supports USB Host, I've found a simple free utility called
USB Host Diagnostics (on Google Play) that you can use to determine if USB Host is supported on your phone and whether it supports the functionality you need. So far, I've found that my Samsung Galaxy S III supports USB stereo headsets and mono microphones, keyboards, mice, flash (thumb) drives, and (of course) my camera. On the other hand, it will not support a Passport external hard drive. I suspect this is because the Passport requires more power than the USB port on the GS III can provide.
Still, that's not that much help if you're considering getting a new Android phone and would like to know (before you commit) whether it will support Helicon Remote. The developer of USB Host Diagnostics is trying to compile a certified list of what phones support what functionality, but every time I've tried to access the database it's hung my PC/browser or phone/browser. Maybe you'll have better luck.
Just thought I'd post that for enlightenment.