I may be dim, I think. I followed the Usage Tutorial for the counting combinator exactly (I believe), but irrespective of which settings I put into the c.c., the output signal is always 'Reset', with whichever value I have set for reset. Step 6: Watch it count! never seems to happen. What am I doing wrong?
PS I set the decider combinator to output the signal named '1' with the value 1, as per the tutorial. Shouldn't it should be the value of the input count, if we're counting the items on the belt?

It's not you, the tutorial is just a little outdated. Just set the Reset to -1 for infinite count or a specific amount to reset at.

If you want, take a screenshot of your setup and settings.

Thanks for the swift response; I had noticed the mention of reset values less than zero, so I'd already tried reset at -1. I have a screenshot done from a sandbox environment, with the object UI's pasted in.
https://www.dropbox.com/s/6hs09oe33fttarw/Counting_Combinator.png?dl=0
You will see that the c.c. output signal is only "Reset" at value -1. In setting this up, I noticed that although I selected Output = Count (and the box has an orange border when selected) the next time I opened the c.c. UI, no output box appears selected, i.e. nothing has an orange border until I select it again.
I'm using Factorio 0.14.22 + Useful Combinators 0.0.5, on Steam, with OS Kubuntu Linux 16.04.
I'm happy to help if this is a bug, and happier if you can point out my silly mistake!

I found the error, it's in the Decider Combinator. You put "1 Signal" instead of "+1 Signal".